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8) An ultimate frisbee team has to order jerseys, shorts, and hats. They have a budget of $1350 to
spend on $50 jerseys, $20 shorts, and $15 hats. They want to buy 40 items in preparation for the
oncoming season and must order as many jerseys as shorts and hats combined. How many of
each item should they order? Write a system of equations to help you solve this problem.

Respuesta :

Answer:

Step-by-step explanation:

By using j, s ,h to represent the number of jerseys,shorts and hats respectively.

System of Equations:

j + s + h = 40

j = s + h

50j + 20s + 15h = 1350

(s + h) + s + h = 40

2s + 2h = 40

s + h = 20

s = 20 – h

50[(20 – h) + h] + 20(20 – h) + 15h = 1350

50(20) + 400 – 20h + 15h = 1350

1400 – 5h = 1350

5h = 50h

h = 10

s = 20 – 10

s = 10

j = 10 + 10

j = 20

20 jerseys, 10 shorts, 10 hats

They order 20 jerseys, 10 shorts, 10 hats

What is system of equation?

A system of equations, also known as a set of simultaneous or equation system, is a finite set of equations for which we sought the common solutions.

According to the question

By using j, s ,h to represent the number of jerseys ,shorts and hats respectively.

System of Equations:

j + s + h = 40.   .   .   .   . Equation (1)

j = s + h.   .   .   .   .   .   .Equation (2)

50j + 20s + 15h = 1350 .    .    .    .     .      .     Equation (3)

By putting the value of j = s + h in equation (1)

(s + h) + s + h = 40

2s + 2h = 40

s + h = 20

s = 20 – h.   .   .   .   .   .   .   .Equation (4)

By putting the value of j = s + h and s = 20 - h in equation (3) we get

50[(20 – h) + h] + 20(20 – h) + 15h = 1350

50(20) + 400 – 20h + 15h = 1350

1400 – 5h = 1350

5h = 50h

h = 10

s = 20 – 10

s = 10

j = 10 + 10

j = 20

Hence , 20 jerseys, 10 shorts, 10 hats

To learn more about system of equation from here

https://brainly.in/question/31127448

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