I'm doing my math homework and I need help.

Question

Juice You bought 12 1-gallon bottles of apple and orange juice for a school dance.
The apple juice was on sale for $1.00 per gallon bottle. The orange juice was $1.75
per 1-gallon bottle. You spent $15.00. Assign labels to the verbal model below. Write
an algebraic model. How many bottles of each type of juice did you buy.

Answer 1

Let x represent apples

let y represent oranges

 

x+y=12

 

x($1)+y($1.75)

x+1.75y=15

 

use elimination method

 

to find y

 

x+1.75y=15

x+  y   =  12

========= subtract

    0.75y=3

 

y=3/0.75=4

 

y=4

 

substitute y to solve for x

 

x+4=12

x=12-4=8

 

to check

8($1)+4($1.75)=

8+7=$15...check

Answer 2

A = bottles of Apple juice

O = bottles of Orange juice

 

from the 1st sentence:

A + O = 12

 

the  cost of each kind:

A * 1.00

C * 1.75

 

we are told the total cost, so:

A + 1.75*O = 15

A = 15 - 1.75*O

 

Sub for A in the 1sr equation:

15 - 1.75*O + O = 12

-0.75*O = -3

 

O =  4

then, from the 1st equation:

A =  8

 

CHECK, using the 2nd equation:

8 + 1.75* 4 = 15 ?

8 + 7 = 15   OK!!