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21 Sep 2021, 05:45
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
87% (02:06) correct
13%
(02:11)
wrong
based on 52
sessions
History
Date
Time
Result
Not Attempted Yet
A collection of 33 coins amounts to $4.35 in face value. If the collection consists of only dimes and quarters, how many dimes are in the collection? (Dime = 10 cents and quarter = 25 cents)
A. 7
B. 14
C. 25
D. 26
E. 27
A. 7
B. 14
C. 25
D. 26
E. 27
21 Sep 2021, 06:41
Kudos
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Bunuel
Let D = the NUMBER of dimes
So, 10D = the VALUE of the dimes (in cents)
Let Q = the NUMBER of quarters
So, 25Q = the VALUE of the quarters(in cents)
The collection amounts to $4.35 in face value.
In other words, the VALUE of the coins is 435 cents.
So we can write: 10D + 25Q = 435
Make our calculations easier let's simplify this equation by dividing both sides by 5 to get: 2D + 5Q = 87
The collection consists of 33 coins
In other words, the total NUMBER of dimes and quarters = 33
We can write: D + Q = 33
How many dimes are in the collection?
In other words, what is the value of D?
We presently have the following system of equations:
2D + 5Q = 87
D + Q = 33
Multiply both sides of the bottom equation by 5 to get:
2D + 5Q = 87
5D + 5Q = 165
Subtract the top equation from the bottom equation to get: 3Q = 78
Solve: Q = 78/3 = 26
Answer: D
11 Jun 2024, 07:50
Kudos
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