algebra word problem

Question

as treasurer of his school’s 4H club, Kenny wants to buy gifts for all 18 members. He can buy t-shirts for $9 and sweatshirts for $15. The club has only $180 to spend. If Kenny wants to spend all of the club’s money, how many of each type of gift can he buy?

Answer 1

Let x = the number of shirts

Let y = the number of sweatshirts

The equations are

x+y=18

9x+15y=180

Solve these by substitution.

Take the first equation and solve for x

x+y=18 Subtract y from both sides

x+y-y=18-y Simplify

x=18-y Plug this into the 2nd equation

9(18-y)+15y=180 Now solve this, start with distribute

162-9y+15y=180 Combine like terms

162+6y=180 Subtract 162 from both sides

162+6y-162=180-162 Simplify

6y=18 divide both sides by 6

6y/6=18/6

y=3

Plug into solve for x

x=18-y

x=18-3

x=15

He should buy 15 shirts and 3 sweatshirts

Answer 2

Hi Doraelle

This is a typical simultaneous equation problem, and we can use the substitution method.

Kenny wants to buy Tshirts and sweatshirts, so let T = # of T-shirts and S= # of sweatshirts

Then T + S = 18 Then, look at the money $9xT + 15xS = $180

From the units equation, I can say T = 18 - S

Next, I substitute 18-S in for T in the money equation

9T +15(18-T) = 180

Reorganizing: 9T + 270 - 15 T - 180 ==> -6T = - 90

Solving T = -144/(-9) = 15

You can figure out S from there, right?