At Frutery, 3 bushels of peaches and 4 bushels of pears cost

Question

At Frutery, 3 bushels of peaches and 4 bushels of pears cost $26.50, and 5 bushels of peaches and 3 bushels of pears cost $35. What is the cost at Frutery of 1 bushel of peaches and 1 bushel of pears?

A. $7
B. $8
C. $9
D. $10
E. $11

obedear · Answer

I couldn't see the way to solve directly for what the question is asking for by multiplying each equation so I used a trick.
3x + 4y = 26.5
5x + 3y = 35

Add the two equations to get:
8x + 7y = 61.5

Divide by 7 to get:

8x/7 + y = 61.5/7

61.5/7 = 8 with some remainder. Since answers are all whole integers, it makes sense to choose answer 8 given that 8 with some remainder is comprised of 8/7 the cost of the peaches.

kevincan · Answer

It makes a lot of sense to reflect on whether we can add or subtract linear equations to get what we want without having to solve for each variable. If we compare the difference of the coefficients in the two equations, it’s easier for us to spot what you were looking for: multiply the first equation by 2

adipisfugat · Answer

Here is the simple and easy way to solve this problem, written in plain text so you can easily copy and paste it:

Let x = the cost of 1 bushel of peaches
Let y = the cost of 1 bushel of pears

Step 1: Write down the two clues from the problem
Clue 1: 3 bushels of peaches + 4 bushels of pears = $26.50
Equation 1: 3x + 4y = 26.50

Clue 2: 5 bushels of peaches + 3 bushels of pears = $35.00
Equation 2: 5x + 3y = 35.00

Step 2: Add the two equations together
If we add everything up, we get:
(3x + 5x) + (4y + 3y) = 26.50 + 35.00
8x + 7y = 61.50

Since 8x and 7y don't have matching numbers, let's try subtracting the smaller equation from the larger one to see if it helps us find a shortcut.

Step 3: Subtract Equation 1 from Equation 2
(5x - 3x) + (3y - 4y) = 35.00 - 26.50
2x - y = 8.50

Rearranging this gives us a simple value for y:
y = 2x - 8.50

Step 4: Substitute y into Equation 2 to find the cost of peaches (x)
5x + 3(2x - 8.50) = 35.00
5x + 6x - 25.50 = 35.00
11x - 25.50 = 35.00

Add 25.50 to both sides:
11x = 60.50

Divide by 11:
x = 5.50
So, 1 bushel of peaches costs $5.50.

Step 5: Find the cost of pears (y)
Plug x = 5.50 back into our simple equation for y:
y = 2(5.50) - 8.50
y = 11.00 - 8.50
y = 2.50
So, 1 bushel of pears costs $2.50.

Step 6: Find the total cost for 1 bushel of each
The question asks for the cost of 1 bushel of peaches and 1 bushel of pears together:
x + y = 5.50 + 2.50 = 8.00

The cost of 1 bushel of peaches and 1 bushel of pears is $8.00.

kevincan · Answer

If we multiply the first equation by 2, we get 6x + 8y = 53

Then we can add the second equation, which is 5x + 3y = 35

We get 11x + 11y =88

Thus x + y = 8

At Frutery, 3 bushels of peaches and 4 bushels of pears cost

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At Frutery, 3 bushels of peaches and 4 bushels of pears cost

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615 to 715 in 15 Days (Ria's Strategies)

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