How many hats and jackets did the club sell?

Question

A club is selling hats and jackets as a fundraiser. Their budget is $1500 and they ordered 270 items. Each hat costs $5 and each jacket costs $8. Let x represent the number of hats and y represent the number or jackets

PLEASE HELP

Answer 1

A club is selling hats and jackets as a fundraiser. Their budget is $1500 and they ordered 270 items. Each hat costs $5 and each jacket costs $8. Let x represent the number of hats and y represent the number or jackets. I ASSUME YOU WANT TO KNOW HOW MANY JACKETS WERE SOLD, AND HOW MANY HATS WERE SOLD.

Let H = number of Hats sold

Let J = number of Jackets sold

H + J = 270 ...and they ordered 270 items

5H + 8J = 1,500 Each hat costs $5 and each jacket costs $8...Their budget is $1,500.

Ella, these are equations of STRAIGHT LINES, and that is why we call them

LINEar Equations.

Let's use the SUBSTITUTION METHOD.

Take the top equation and solve for H:

H + J = 270 (Top Equation)

H + J - J = 270 - J

H = 270 - J

Now, substitute 270 - J into the second equation every time we see an "H".

5H + 8J = 1,500 (Bottom Equation)

5(270 - J) + 8J = 1,500 Notice we now have ONLY ONE VARIABLE "J".

1,350 - 5J + 8J = 1,500 Multiplying 5 times 270 and - J.

1,350 + 3J = 1,500 Combining like terms(J).

1,350 - 1,350 + 3J = 1,500 - 1,350 Subtracting 1,350 from both sides.

3J = 150

3J/3 = 150/3 Dividing both sides by 3.

J = 50

ANSWER 1: They sold 50 JACKETS

Plug 50 into "J" in either of the two equations to solve for H, the number of hats.

H + J = 270

H + 50 = 270

H + 50 - 50 = 270 - 50

H = 220

ANSWER 2: They sold 220 HATS.

CHECKING:

Top Equation: H + J = 270

220 + 50 = 270 Yes!

Bottom Equation: 5H + 8J = 1,500

5(220) + 8(50) = 1,100 + 400 = 1,500 Yes!

Hope this helps you Ella.