Question

At a sale on winter clothing, Cody bought 2 pairs of gloves and 4 hats for $43.00. Tori bought 2 pairs of gloves and 2 hats for $30.00. Find the cost of each.

Answer 1

The cost of one pair of gloves is $8.50 and one hat is $6.50

Step-by-step explanation:

Let,

Cost of each pair of gloves = x

Cost of each hat = y

According to given statement;

2x+4y=43     Eqn 1

2x+2y=30     Eqn 2

Subtracting Eqn 2 from Eqn 1

$(2x+4y)-(2x+2y)=43-30\\2x+4y-2x-2y=13\\2y=13$

Dividing both sides by 2

$\frac{2y}{2}=\frac{13}{2}\\y=6.50$

Putting y=6.5 in Eqn 1

$2x+4(6.50)=43\\2x+26=43\\2x=43-26\\2x=17$

Dividing both sides by 2

$\frac{2x}{2}=\frac{17}{2}\\x=8.50$

The cost of one pair of gloves is $8.50 and one hat is $6.50

Keywords: linear equation, elimination method

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