Suppose a little girl likes peanut butter and jelly sandwiches with exactly 2T of jelly and 1T of peanut butter.Suppose further that her mom agrees to make sandwiches to those exact specifications and the price of peanut butter is $.25/T and the price of jelly is $.10/T.If she has $1.8 to spend on peanut butter and jelly ingredients (ignore the bread)in a week,how many sandwiches will she make?

Question

Quizplus · Accepted Answer

Let's set up the following system of equations:

2j + p = 1.8  (where j is the cost of 2 tablespoons of jelly and p is the cost of 1 tablespoon of peanut butter)

0.1j = cost of 2T of jelly
0.25p = cost of 1T of peanut butter

We can solve for j and p by substituting the second set of equations into the first:

2(0.1j) + 0.25p = 1.8

0.2j + 0.25p = 1.8

Next, we can multiply the second equation by -2 and add it to the first:

-0.5p = -1.2

p = 2.4

Now we can substitute p back into one of our original equations to solve for j:

2j + 2.4 = 1.8

2j = -0.6

j = -0.3 (which doesn't make sense since we can't have negative prices)

This means that there is no solution to the system of equations, which implies that the amount of money we have is not enough to make a single sandwich. However, we can see that the cost of the ingredients for one sandwich is 2(0.1) + 0.25 = 0.45, which is less than the total amount we have to spend. Therefore, we can make at least one sandwich. The closest option to this is option C, which gives us 4 sandwiches for a total cost of 4(0.45) = 1.8. Therefore, the best choice is:

Answer: C

Suppose a Little Girl Likes Peanut Butter and Jelly Sandwiches