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)

Question

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.)

Solve the system using your chosen method

Answer 1

Let's use the substitution method to solve the system of equations. We can start by solving the first equation for x or y:

x = 78 - y

Now we can substitute this expression for x into the second equation:

(78 - y)/3 = (78 - y)/4

Now we can solve the equation for y. Start by multiplying both sides of the equation by 12 to get rid of the fractions:

4(78 - y) = 3(78 - y)

Expand:

312 - 4y = 234 - 3y

Now, add 4y to both sides and subtract 234 from both sides:

78 = y

Now that we have a value for y, we can substitute it back into our expression for x:

x = 78 - 78 = 0

So, Rika should hand out 0 more fragrance samples (x) and 78 more hand lotion samples (y).