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Fed [463]
3 years ago
7

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:
aalyn [17]3 years ago
8 0

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

Step-by-step explanation:

Hats and mittens are on sale at the store!

  • One woman was able to buy 5 hats and 4 pairs of mittens for $30
  • Another woman purchased 3 pairs of mittens and 2 hats for $19
  • The price of one hat is x
  • The price of one pair of mittens is y

We need to find x and y

∵ One woman was able to buy 5 hats and 4 pairs of mittens for $30

∵ The price of one hat is x

∵ The price of one pair of  mittens is y

- Multiply 5 hats by x and 4 pairs of mittens by y and equate

  their sum by 30

∴ 5x + 4y = 30 ⇒ (1)

∵ Another woman purchased 3 pairs of mittens and 2 hats for $19

- Multiply 2 hats by x and 3 pairs of mittens by y and equate

  their sum by 19

∴ 2x + 3y = 19 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -2 and equation (2) by 5 to eliminate x

∵ -10x - 8y = -60 ⇒ (3)

∵ 10x + 15y = 95 ⇒ (4)

- Add equations (3) and (4)

∴ 7y = 35

- Divide both sides by 7

∴ y = 5

Substitute the value of y in equation (1) or (2) to find x

∵ 2x + 3(5) = 19

∴ 2x + 15 = 19

- Subtract 15 from both sides

∴ 2x = 4

- Divide both sides by 2

∴ x = 2

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

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

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