Question

if 7 marshmallows and 11 lollipops cost $1.93 altogether, and 11 marshmallows and 7 lollipops cost $2.21 altogether, then how many cents does 1 lollipop cost?

Answer 1

8 cents

Explanation:

You want the cost of 1 lollipop when ...

• 7 marshmallows and 11 lollipops are $1.93
• 11 marshmallows and 7 lollipops are $2.21

Setup

The equations representing these purchases can be written as ...

7M +11L = 1.93

11M +7L = 2.21

Solution

Multiplying the first equation by 11 and subtracting 7 times the second equation, we have ...

11(7M +11L) -7(11M +7L) = 11(1.93) -7(2.21)

72L = 5.76 . . . . . . . simplify

L = 0.08 . . . . . . . . divide by 72

One lollipop costs 8 cents.