Question

Hats and mittens are on sale at the store! One woman was able to buy 5 hats and 4 pairs of mittens for $30.

Answer 1

The price of one hat is $2 and price of one pair of mittens is $5.

Step-by-step explanation:

Let,

Price of one hat = x

Price of one pair of mittens = y

According to given statement;

5x+4y=30      Eqn 1

2x+3y=19       Eqn 2

Multiplying Eqn 1 by 2

$2(5x+4y=30)\\10x+8y=60\ \ \ \ Eqn\ 3$

Multiplying Eqn 2 by 5

$5(2x+3y=19)\\10x+15y=95\ \ \ \ Eqn\ 4$

Subtracting Eqn 3 from Eqn 4

$(10x+15y)-(10x+8y)=95-60\\10x+15y-10x-8y=35\\7y=35$

Dividing both sides by 7

$\frac{7y}{7}=\frac{35}{7}\\y=5$

Putting y=5 in Eqn 1

$5x+4(5)=30\\5x+20=30\\5x=30-20\\5x=10$

Dividing both sides by 5

$\frac{5x}{5}=\frac{10}{2}\\x=2$

The price of one hat is $2 and price of one pair of mittens is $5.

Keywords: linear equation, subtraction

Learn more about linear equations at:

• brainly.com/question/11145277
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