Question

Ms. Betty was supposed to make 4 bag and 5 aprons with 8.22 yards of cloth. Instead, she made 5 bags and 4 aprons and only needed 7.44 yards of cloth. How much cloth was needed altogether to make 2 bags?

Answer 1

0.96 yards of cloth was needed to make 2 bags.

Step-by-step explanation:

Let,

x be the yards of cloth used for each bag

y be the yards of cloth used of each apron

According to given statement

4x+5y=8.22      Eqn 1

5x+4y=7.44      Eqn 2

Multiplying Eqn 1 by 5

$5(4x+5y=8.22)\\20x+25y=41.10\ \ \ Eqn\ 3$

Multiplying Eqn 2 by 4

$4(5x+4y=7.44 )\\20x+16y=29.76\ \ \ Eqn\ 4$

Subtracting Eqn 4 from Eqn 3

$(20x+25y)-(20x+16y)=41.10-29.76\\20x+25y-20x-16y=11.34\\9y=11.34$

Dividing both sides by 9

$\frac{9y}{9}=\frac{11.34}{9}\\y=1.26$

Putting y=1.26 in Eqn 1

$4x+5(1.26)=8.22\\4x+6.30=8.22\\4x=8.22-6.30\\4x=1.92$

Dividing both sides by 4

$\frac{4x}{4}=\frac{1.92}{4}\\x=0.48$

Cloth required for one bag = 0.48 yards

Cloth required for 2 bags = 0.48*2 = 0.96 yards

0.96 yards of cloth was needed to make 2 bags.

Keywords: linear equation, elimination method

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