SOLUTION: Jim spends $21 on some liquid refreshments. The orange soda costs twice as much as the pineapple juice, which costs twice as much as the chocolate milk. How much was the pineapple

Hi, there--

PROBLEM--
Jim spends $21 on some liquid refreshments. The orange soda costs twice as much as the 
pineapple juice, which costs twice as much as the chocolate milk. How much was the pineapple
juice?

SOLUTION--
Let p be the cost of the pineapple juice (in dollars)
Let o be the cost of the orange soda (in dollars)
Let m be the cost of the chocolate milk (in dollars)


Jim spends $21 on drinks all together, so
p + o + m = 21

The orange soda costs twice as much as the pineapple juice, so
o = 2p

The pineapple juice costs twice as much as the chocolate milk, so
p = 2m

We have three equations with three variables. Solve the system.
p  + o + m = 21
o = 2p
p = 2m.

We will use the substitution method. Rewrite the third equation in "m equals" form.

p = 2m
m = (1/2)p

Substitute 2p for o and (1/2)p for m in the first equation.
p + o + m = 21
p + 2p + (1/2)p = 21

Solve for p.
(7/2)p = 21

Multiply both sides of the equation by 2/7 (the reciprocal of 7/2.)

p = 21 * (2/7)
p = 6

In the context of this problem, the equation p = 6 means that the pineapple juice costs $6.

To find the cost of the orange soda:
o = 2p
o = 2(6)
o = 12
The cost of the orange soda is $12.

To find the cost of chocolate milk
p = 2m
6 = 2m
m = 3
The cost of the chocolate milk is $3.

The cost of all the drinks is $21. Check this--12+6+3 = 21.

That's it.

Mrs.Figgy