Question

rika gives away samples of a new fragrance and a new scented hand lotion to customers. she must hand out a total of 114 samples during her shift she has already handed out 36 samples which represent 1/3 the number of fragrances samples and 1/4 the number of hand lotion samples she must hand out, write a system of equations for this problem situation.

Answer 1

Let F be the number of fragrance samples and L be the number of hand lotion samples.

We know that F + L = 114, since Rika must hand out a total of 114 samples.

We also know that F = (1/3)L and L = (1/4)F, since the number of fragrance samples is 1/3 of the number of hand lotion samples, and the number of hand lotion samples is 1/4 of the number of fragrance samples.

Substituting the second equation into the first equation, we get:

F + (1/4)F = 114

Combining like terms, we get:

(5/4)F = 114

Dividing both sides by (5/4), we get:

F = 92

Substituting this value back into the second equation, we get:

L = (1/4)(92) = 23

Therefore, the system of equations is:

F + L = 114

F = (1/3)L

L = (1/4)F

The solution to this system is F = 92 and L = 23