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

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.

90

.8+.5 (100-x)=77

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

To find the number of people who liked the skin cream, we can use the information given in the question and set up an equation.

Let's say the number of people who liked the skin cream is x.

From the given information, we know that 80% of the people who liked the skin cream also liked the lip balm. So, 80% of x people is (80/100) * x = 0.8x.

We also know that 50% of the people who did not like the skin cream liked the lip balm. So, 50% of the people who did not like the skin cream is (50/100) * (100 - x) = 0.5(100 - x).

According to the question, 77 people liked the lip balm, which includes people who liked both the skin cream and the lip balm. So, we can write the equation:

0.8x + 0.5(100 - x) = 77

Simplifying this equation, we get:

0.8x + 50 - 0.5x = 77

Combining like terms, we have:

0.3x + 50 = 77

Subtracting 50 from both sides, we get:

0.3x = 27

Dividing both sides by 0.3, we find:

x = 27 / 0.3 = 90

So, 90 people liked the skin cream.