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 fragrance samples and
_1
4 the number of hand lotion samples she must hand out.
Write a system of equations for this problem situation. Let x represent the number
of fragrance samples, and let y represent the number of hand lotion samples.
The system of equations would be:
x + y = 78 (since Rika has to hand out a total of 114 samples, and she has already handed out 36 samples, which leaves 78 samples to hand out)
x/3 = (78-y)/4 (since Rika must hand out _1
3 the number of fragrance samples and _1
4 the number of hand lotion samples she must hand out. So, x/3 represents the number of fragrance samples she must hand out and (78-y)/4 represents the number of hand lotion samples she must hand out. We set these two expressions equal to each other since they represent the same thing - the total number of samples she has to hand out.)