# I am having a problem with word problems that are solving applied problems. Three equations.?

Starbucks sells cappuccinos in three sizes: tall for \$2.65, grande for \$3.20, and vente for \$3.50. After a rally Bruce served 50 cappuccinos. The number of tall and vente cappuccinos, combined, was 2 fewer than the number of grande cappuccinos. If he collected a total of \$157, how many cappuccinos of each size did he serve?

x=tall, y=grande, z=vente

1.) x + y + z = 50

2.) x + z = y - 2

I know 1.) is right, not sure about 2.), and I can't figure the third one.

Can anyone help me out?

Relevance

Your first two equations are correct.

For the third equation, think of it this way:

- How much does Bruce get for selling talls? 2.65*x.

- How much does Bruce get for selling grandes? 3.20*y.

- How much does Bruce get for selling ventes? 3.50*z.

You know that the total amount of money collected is \$157.

Obviously, you get the total amount by adding up the amounts Bruce gets for selling talls, grandes, and ventes.

Hence, your third equation is: 2.65x + 3.20y + 3.50z = 157.

Hope that helps!

• 1 and 2 are fine. the third should be

2.65x + 3.20y + 3.50z = 157

because you know the cost of each and the total amount collected. :)

• You are correct so far!

The 3rd equation connecting x, y and z is

\$2.65x + \$3.20y + \$3.50z = \$157

• 2.65x + 3.20y + 3.50z = 157

1st equation

(x + z) = y - 2

2nd equation

x+ y + z = 50

replace x and z

( x + z ) + y = 50

y - 2 + y = 50

2y - 2 = 50

2y = 52

y = 26

plug in y

2.65x + 3.2y + 3.5z = 157

2.65x + 83.2 + 3.5z = 157

2.65x +3.5z = 73.8