Write a system of equations from word problems

Question

Question: Kylie went into a grocery store and bought 3 apples and 4 bananas, costing a total of $6.50. Lily went into the same grocery store and bought 10 apples and 5 bananas, costing a total of $17.50. Write a system of equations that could be used to determine the price of each apple and the price of each banana.

Answer 1

3A + 4B = 6.5

10A + 5B = 17.5

multiply 1st equation by 5, 2nd by 4, then subtract to eliminate one variable, then solve for the other variable

40A + 20B = 70

15A +20B = 32.5

25A = 37.5

A = 37.5/25 = $1.50 per apple

B =[6.5-3(1.5)]/4 =1/2 = $.50 = 50 cents per banana

check the answers, if you don't go bananas first

3(1.5) + 4(.5) = 4.5 +2 = 6.5

10(1.5) +5(.5) = 15 +2.5 = 17.5

Answer 2

3a + 4b = 6.50

10a + 5b = 17.50

Answer 3

Let's let a be the price of an apple and b be the price of a banana. Then the two equations are:

3a + 4b = 6.50

10a + 5b = 17.50