Question

Shopping at clothing world, jenna buys her children four shirts and three pairs of pants for 124.25. She returns the next day and buys three shirts and five pair of pants for 161.25. What is the price of each shirt and each pair of pants?

Answer 1

The cost of one shirt is 12.50 and cost of one pair of jeans is 24.75

Step-by-step explanation:

Let,

Cost of one shirt = x

Cost of pair of jeans = y

According to given statement;

4x+3y=124.25    Eqn 1

3x+5y=161.25     Eqn 2

Multiplying Eqn 1 by 3

$3(4x+3y=124.25)\\12x+9y=372.75\ \ \ Eqn\ 3$

Multiplying Eqn 2 by 4

$4(3x+5y=161.25)\\12x+20y=645\ \ \ Eqn\ 4$

Subtracting Eqn 3 from Eqn 4

$(12x+20y)-(12x+9y)=645-372.75\\12x+20y-12x-9y=272.25\\11y=272.25$

Dividing both sides by 11

$\frac{11y}{11}=\frac{272.25}{11}\\y=24.75$

Putting 24.75 in Eqn 1

$4x+3(24.75)=124.25\\4x+74.25=124.25\\4x=124.25-74.25\\4x=50$

Dividing both sides by 4

$\frac{4x}{4}=\frac{50}{4}\\x=12.50$

The cost of one shirt is 12.50 and cost of one pair of jeans is 24.75

Keywords: linear equation, elimination method

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