A marketing company asked 100 people whether they liked a new skin cream and lip balm. The company found that 80% of the people who liked the new skin cream also liked the new lip balm, and that 50% of the people who did not like the new skin cream liked the new lip balm. If 77 people liked the lip balm, how many people liked the skin cream?

Question

A marketing company asked 100 people whether they liked a new skin cream and lip balm. The company found that 80% of the people who liked the new skin cream also liked the new lip balm, and that 50% of the people who did not like the new skin cream liked the new lip balm. If 77 people liked the lip balm, how many people liked the skin cream?
___  people

MathMate · Answer

First observation:
People either liked the skin cream (x of them) or didn't like the skin cream (100-x of them).

"80% of the people who liked the new skin cream also liked the new lip balm"
that makes 0.8x liked new lip balm.

"50% of the people who did not like the new skin cream liked the new lip balm"
that makes 0.5(100-x) of them.

Total=0.8x+0.5(100-x)=77
Solve for x.

bill · Answer

90

monalisa · Answer

.8+.5 (100-x)=77 .8+50-.5x=77 -.5x=77-50.8 -.5x=26.2 -.5x/-.5=26.2/-.5 x=-52.4