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german
3 years ago
9

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

Mathematics
1 answer:
morpeh [17]3 years ago
4 0

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
  • brainly.com/question/11150876

#LearnwithBrainly

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