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12. A summer soccer camp ordered a total of 84 soccer balls and t-shirts for the season. Soccer balls cost $25 each and t-shirts cost $9.50 each. If they payed $1,046 total for the purchase, how many of each item was ordered?

Respuesta :

semsee45

Answer:

16 Soccer balls

68 T-shirts

Step-by-step explanation:

Given information:

  • Total order = 84 items
  • Cost of a soccer ball = $25
  • Cost of a t-shirt = $9.50
  • Total bill = $1,046

Define the variables:

  • Let x = the number of soccer balls ordered.
  • Let y = the number of t-shirts ordered.

Create two equations from the given information:

[tex]\textsf{Equation 1}: \quad x + y = 84[/tex]

[tex]\textsf{Equation 2}: \quad 25x+9.5y=1046[/tex]

Rewrite Equation 1 to make y the subject:

[tex]\implies y=84-x[/tex]

Substitute this into Equation 2 and solve for x:

[tex]\implies 25x+9.5(84-x)=1046[/tex]

[tex]\implies 25x+798-9.5x=1046[/tex]

[tex]\implies 15.5x+798=1046[/tex]

[tex]\implies 15.5x=248[/tex]

[tex]\implies x=16[/tex]

Substitute the found value of x into the rewritten form of Equation 1 and solve for y:

[tex]\implies y=84-16[/tex]

[tex]\implies y=68[/tex]

Solution

  • Soccer balls ordered = 16
  • T-shirts ordered = 68

Learn more about systems of equations here:

https://brainly.com/question/28281431

https://brainly.com/question/27034625

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