One jar of peanut butter and 3 loaves of bread cost $6.70. Three jars of peanut butter and 1 loaf of bread cost $9.32. Find the cost of a jar of peanut butter and a loaf of bread.

Question

One jar of peanut butter and 3 loaves of bread cost $6.70. Three jars of peanut butter and 1 loaf of bread cost $9.32. Find the cost of a jar of peanut butter and a loaf of bread.

Answer 1

Let us call the jar of peanut butter "P"

Let us call the loaf of bread "L"

Now let us make some mathematical sentences from the information provided to us from the question above.

1P + 3L = $6.70
3P + 1L = $9.32

As you can see, we have 2 unknowns. We want to either add or subtract the 2 sentences from each other so that we're only left with 1 unknown.

If we multiply the 1st sentence by 3, I notice that we will have 3P and 9L, therefore when we subtract sentence 1 from sentence 2, we'll only be left with "L"

1P + 3L = $6.70
3(1P + 3L) = 3($6.70)
3P + 9L = $20.10

3P + 1L = $9.32

Now let us subtract the new sentence 1 from sentence 2.

3P + 9L - (3P + 1L) = $20.10-$9.32
3P + 9L - 3P - 1L = $10.78
9L-1L = $10.78
8L = $10.78
L = $10.78/8
L = $1.35

Now you can plug in the value for "L" back into one of the 2 sentences and solve for the "P".

Answer 2

What is the ratio, but NOT the unit rate if Mary makes a peanut butter and jelly sandwich with 2 parts peanut butter and 3 parts jelly?

Answer 3

To solve this problem, let's denote the cost of a jar of peanut butter as "P" and the cost of a loaf of bread as "B". We can set up two equations based on the information given:

Equation 1: P + 3B = 6.70 (one jar of peanut butter and 3 loaves of bread cost $6.70)
Equation 2: 3P + B = 9.32 (three jars of peanut butter and 1 loaf of bread cost $9.32)

We now have a system of two equations with two variables. To find the values of P and B, we can solve this system using a method called substitution:

Step 1: Solve Equation 1 for P:
P = 6.70 - 3B

Step 2: Substitute the value of P from Step 1 into Equation 2:
3(6.70 - 3B) + B = 9.32

Step 3: Distribute:
20.10 - 9B + B = 9.32

Step 4: Combine like terms:
20.10 - 8B = 9.32

Step 5: Move the constant term to the other side of the equation:
-8B = 9.32 - 20.10

Step 6: Simplify:
-8B = -10.78

Step 7: Divide both sides by -8 to solve for B:
B = -10.78 / -8 = 1.35

Now, we have the cost of a loaf of bread (B = $1.35). To find the cost of a jar of peanut butter (P), we can substitute this value of B back into Equation 1:

P + 3(1.35) = 6.70
P + 4.05 = 6.70
P = 6.70 - 4.05
P = 2.65

Thus, a jar of peanut butter costs $2.65 and a loaf of bread costs $1.35.