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In a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. If one
sweater and four shirts cost $45, while four sweaters and three shirts cost $76, find the price of one sweater and the price of one shirt.

The price of one sweater is $__

and the price of one shirt is $__
(Simplify)

Answer :

THELEANGREENBEANIN

Key Concepts

  • Systems of equations word problems

Solving the Question

Let the price of sweaters be x and the price of shirts be y.

We're given:

  • x + 4y = $45
  • 4x + 3y = $76

We can solve using substitution, where we input one equation into the other.

⇒ Isolate x in the first equation:

[tex]x + 4y = 45\\x = 45 - 4y[/tex]

⇒ Plug this as x in the second equation:

[tex]4x + 3y = 76\\4(45 - 4y) + 3y = 76\\180 - 16y + 3y = 76\\180 - 13y = 76\\- 13y = -104\\y=8[/tex]

Therefore, y = 8. Plug this into one of the equations and solve for x:

[tex]x = 45 - 4y\\x = 45 - 4(8)\\x = 45 - 32\\x =13[/tex]

Therefore, x = 13.

Answer

y = 8

x = 13

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