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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75 17 Sep 2017, 13:45
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25% (medium)

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85% (02:34) correct 15% (02:40) wrong based on 259 sessions

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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75. If the 5-cent coins were replaced with 10-cent coins and the 10-cent coins were replaced with 5-cent coins, the coins would be worth a total of $2.15. How many coins are in the purse?

A. 26
B. 27
C. 28
D. 29
E. 30
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A
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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75 17 Sep 2017, 18:28
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Let the number of 5 cent coins be a and the number of 10 cent coins be b

we have been give 5a + 10b = 175 (total value in cents)
on reversing the numbers we get 5b + 10a = 215 (total value in cents)
add both the equations to get 15(a + b) = 390
therefore a + b = 26

Answer is (A)
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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75 17 Sep 2017, 19:53
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Let the total 5 cent coins be x, and the 10 cent coins be y

From the question stem, \(5x + 10y = 175\)
Value of y(by the following equation) : \(y = \frac{175 - 5x}{10}\)

Substituting this value of y in the second equation
\(10x + \frac{5(175 - 5x)}{10} = 215\)
\(100x + 875 - 25x = 2150\)
\(75x = 1275\)
\(x = 17\)

Substituting this value of x in equation\(5x+10y = 175\)
\(85 + 10y = 175\)
\(y = 9\)

Therefore the sum of coins in the p = 17 + 9 = 26(Option A)
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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75 17 Sep 2017, 21:26
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Gnpth
A purse contains 5-cent coins and 10-cent coins worth a total of $1.75. If the 5-cent coins were replaced with 10-cent coins and the 10-cent coins were replaced with 5-cent coins, the coins would be worth a total of $2.15. How many coins are in the purse?

A. 26
B. 27
C. 28
D. 29
E. 30
Show more
I solved with two variables, and it works, but I have a question about my own method that applies to vishalbalwani 's method, too.

Let A = the number of 5-cent coins
Let B = the number of 10- cent coins

In one scenario, the coins, in their respective unknown quantities, total $1.75

In a second scenario, the 5-cent coins and 10-cent coins exchange quantities exactly, and they total $2.15

5A + 10B = 175 (P)
10A + 5B = 215 (Q)

Multiply (Q) by two, and subtract (P)

20 A + 10B = 430
__5A + 10B = 175
15A = 255
A = 17

There are 17 coins worth 5 cents.

Use (P) to find the number of 10-cent pieces

5(17) + 10B = 175
10B = 90
B = 9
There are 9 coins worth 19
0 cents.

A = 17, B = 9, total = 26 coins

Answer A

I have run this problem three ways, including vishalbalwani 's, and working from answer choices. This combination (number of coins), is the only one that works.

Question: Is the method sound? The variables work, but they seem inconsistent.

I use A as a quantity for 5-cent coins. The coefficients of the variables -- 5 and 10 -- are the values of the coins in cents.

But in the second equation, (Q) I do not think I have switched quantities, per the prompt. I think have switched values. In the second equation, (Q), the 5, a value, is in front of B -- which is supposed to be the quantity of 10-cent coins. vishalbalwani did the same.

What am I missing? We are supposed to be switching quantities. But switching values works.

I think pushpitkc avoids the whole problem by immediately defining y in terms of x from one equation.

Is my method sound?
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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75 22 Sep 2017, 07:49
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Gnpth
A purse contains 5-cent coins and 10-cent coins worth a total of $1.75. If the 5-cent coins were replaced with 10-cent coins and the 10-cent coins were replaced with 5-cent coins, the coins would be worth a total of $2.15. How many coins are in the purse?

A. 26
B. 27
C. 28
D. 29
E. 30
Show more

We can create two equations in which a = the initial number of 5-cent coins and b = the initial number of 10-cent coins. We can create the “money” equation by recalling that a 5-cent coin is $0.05 and a 10-cent coin is $0.10; thus:

0.05a + 0.1b = 1.75

And, after we reverse the coinage, we have:

0.1a + 0.05b = 2.15

Multiplying the first equation by -2, we have:

-0.1a - 0.2b = -3.50

Adding the two equations, we have:

-0.15b = -1.35

b = 9

Thus:

0.05a + (0.1)(9) = 1.75

0.05a = 0.85

a = 17

So, there is a total of 17 + 9 = 26 coins.

Answer: A
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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75 22 Sep 2017, 08:38
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Gnpth
A purse contains 5-cent coins and 10-cent coins worth a total of $1.75. If the 5-cent coins were replaced with 10-cent coins and the 10-cent coins were replaced with 5-cent coins, the coins would be worth a total of $2.15. How many coins are in the purse?

A. 26
B. 27
C. 28
D. 29
E. 30
We can create two equations in which a = the initial number of 5-cent coins and b = the initial number of 10-cent coins. We can create the “money” equation by recalling that a 5-cent coin is $0.05 and a 10-cent coin is $0.10; thus:

0.05a + 0.1b = 1.75

And, after we reverse the coinage, we have:

0.1a + 0.05b = 2.15

Multiplying the first equation by -2, we have:

-0.1a - 0.2b = -3.50

Adding the two equations, we have:

-0.15b = -1.35

b = 9

Thus:

0.05a + (0.1)(9) = 1.75

0.05a = 0.85

a = 17

So, there is a total of 17 + 9 = 26 coins.

Answer: A
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ScottTargetTestPrep , where you reverse the coinage, what do variables \(a\) and \(b\) stand for? (I had the same question about my own method, above.)

Perhaps the variables stand simply for the total number of coins, and absent any total number of coins, we cannot write one variable in terms of another.

Conceptually, however, that reasoning does not make a lot of sense to me.

We have two unknown quantities in two scenarios. In the first equation, the quantity b is defined as the number of $0.10 coins (and qty "a" initially is # of $.05 coins)

If "b" then switches to the number of $0.05 coins (vice versa for "a"), how are those two a's and b's the same, such that we can use them as an identity in solving two equations?

Sorry if this question is sophomoric; usually I can find my way out of a muddle. Not this time.
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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75 22 Sep 2017, 09:04
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Gnpth
A purse contains 5-cent coins and 10-cent coins worth a total of $1.75. If the 5-cent coins were replaced with 10-cent coins and the 10-cent coins were replaced with 5-cent coins, the coins would be worth a total of $2.15. How many coins are in the purse?

A. 26
B. 27
C. 28
D. 29
E. 30
Show more


Hi....

A logical way...

When you interchange, the total amount increases, so 5-cents are more.
How much ? Say x, so 5x=215-175=40... X=8...

So initial amount is 5(y+8)+10y=175.....15y+40=175.....15y=135....y=9
Total coins = y+8+y=9+8+9=26

A
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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75 01 Oct 2017, 12:26
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ScottTargetTestPrep
Gnpth
A purse contains 5-cent coins and 10-cent coins worth a total of $1.75. If the 5-cent coins were replaced with 10-cent coins and the 10-cent coins were replaced with 5-cent coins, the coins would be worth a total of $2.15. How many coins are in the purse?

A. 26
B. 27
C. 28
D. 29
E. 30
We can create two equations in which a = the initial number of 5-cent coins and b = the initial number of 10-cent coins. We can create the “money” equation by recalling that a 5-cent coin is $0.05 and a 10-cent coin is $0.10; thus:

0.05a + 0.1b = 1.75

And, after we reverse the coinage, we have:

0.1a + 0.05b = 2.15

Multiplying the first equation by -2, we have:

-0.1a - 0.2b = -3.50

Adding the two equations, we have:

-0.15b = -1.35

b = 9

Thus:

0.05a + (0.1)(9) = 1.75

0.05a = 0.85

a = 17

So, there is a total of 17 + 9 = 26 coins.

Answer: A
ScottTargetTestPrep , where you reverse the coinage, what do variables \(a\) and \(b\) stand for? (I had the same question about my own method, above.)

Perhaps the variables stand simply for the total number of coins, and absent any total number of coins, we cannot write one variable in terms of another.

Conceptually, however, that reasoning does not make a lot of sense to me.

We have two unknown quantities in two scenarios. In the first equation, the quantity b is defined as the number of $0.10 coins (and qty "a" initially is # of $.05 coins)

If "b" then switches to the number of $0.05 coins (vice versa for "a"), how are those two a's and b's the same, such that we can use them as an identity in solving two equations?

Sorry if this question is sophomoric; usually I can find my way out of a muddle. Not this time.
Show more

The variables a and b stand for the initial number of 5- and 10-cent coins, before and after reversing the coinage. The only thing that changes when the coinage is reversed is that the number of 5-cent coins is now b and the number of 10-cent coins is now a.
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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75 13 Jul 2026, 11:59
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ScottTargetTestPrep,
Can you please explain why 1.75 is being converted to 175?Didn't understand the conversion
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A purse contains 5-cent coins and 10-cent coins worth a total of $1.75 14 Jul 2026, 11:04
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Hi sarkarsarbani,

Good question, and it's all about keeping the units the same on both sides of the equation.

Look at the equation the earlier posts wrote:

5a + 10b = 175

Here the 5 and the 10 are the values of the coins measured in cents, not dollars - a 5-cent coin and a 10-cent coin. So the left side of the equation is a total measured in cents.

That means the right side has to be in cents too. You can't have cents on one side and dollars on the other - the two sides wouldn't match.

Since $1 = 100 cents, you just convert the dollar total into cents:

- $1.75 × 100 = 175 cents
- $2.15 × 100 = 215 cents

That's the only reason 1.75 becomes 175 - it's the same amount of money, just written in cents so it lines up with the 5 and 10.

(You could instead keep everything in dollars, like ScottTargetTestPrep did: 0.05a + 0.10b = 1.75. That also works - notice he used 0.05 and 0.10[/b> for the coin values so both sides stay in dollars. Same idea, just a different unit. Most people prefer cents because it avoids the decimals.)

Quick way to remember it: before you set up a money equation, pick one unit - all cents or all dollars - and force every number into that unit.

Try it: if a total is $3.40, how many cents is that? Multiply by 100 → 340 cents. Same logic every time.

Answer: A

sarkarsarbani
ScottTargetTestPrep,
Can you please explain why 1.75 is being converted to 175?Didn't understand the conversion
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