Two florists purchased flower bouquets and vases at the same store.
The first florist bought 3 flower bouquets and 5 vases for a total of $25.75. The second florist bought 8 flower bouquets and 2 vases for a total of $29.00.

What is the price of a flower bouquet?

Enter your answer in the box.
$_____

Question

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15-05-2017
Mathematics

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Two florists purchased flower bouquets and vases at the same store.
The first florist bought 3 flower bouquets and 5 vases for a total of $25.75. The second florist bought 8 flower bouquets and 2 vases for a total of $29.00.

What is the price of a flower bouquet?

Enter your answer in the box.
$_____

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JcAlmighty JcAlmighty · Answer 1 · 2017-05-22T10:23:46+02:00

The answer is:
flower bouqet = $2.75
vase = $3.50

x - the number of flower bouquets
y - the number of vases

The first florist bought 3 flower bouquets and 5 vases for a total of $25.75:
3x + 5y = 25.75

The second florist bought 8 flower bouquets and 2 vases for a total of $29.00:
8x + 2y = 29

This is the system of two equations:
3x + 5y = 25.75
8x + 2y = 29
____
Divide the second equation by 2:
3x + 5y = 25.75
4x + y = 14.50
____
Express the second equation in the terms of y:
3x + 5y = 25.75
y = 14.50 - 4x
____
Substitute y in the first equation:
3x + 5(14.50 - 4x) = 25.75
3x + 72.50 - 20x = 25.75
-17x = 25.75 - 72.50
-17x = -46.75
x = -46.75/-17
x = $2.75

y = 14.50 - 4 * 2.75
y = 14.50 - 11
y = $3.50