Julio and david were in target and decided to check out the clearance section. they found pencils and erasers that were on sale and decided to buy some. julio bought 4 pencils and 3 erasers for $0.37 and david paid $0.33 for 3 pencils and 4 erasers. what is the cost of one pencil? what is the cost of one eraser?

p=0.07 and e=0.03

Step-by-step explanation:

This is a typical problem of 2-equation system with 2 unknown variables. Lets first think about it.

Julio bought 4 pencils at a price of p each and 3 erasers at a price of e each at a cost of 0.37 (from here I will omit the $ symbol for simplicity). So we could write an equation of the form:

4p + 3e = 0.37

David paid 0.33 for 3 pencils and 4 erasers, paying the same prices as Julio:

3p + 4e = 0.33

So, we have a 2-equation system with two unknowns p and e:

4p + 3e = 0.37 [eq 1]

3p + 4e = 0.33 [eq 2]

Take equation 1 and multiply it by 3 and take equation 2 and multiply it by -4. As me multiply every term of each equation the equation maintains:

4p + 3e = 0.37 (x3)      12p + 9e = 1.11

3p + 4e = 0.33 (x -4)   -12p - 16e = -1.32

Now, sum both equations, summing term by term, i.e., the p's together and the e's  together:

(12p - 12p) + (9e - 16e) = 11.1 -1.32

-7e = -0.21

Divide both sides by (-7):

-7e/(-7) = -0.21/(-7)

e = 0.03

So, the cost of 1 eraser is $0.03. Now, replace it value in eq 1 or eq2 to find p:

4p + 3e = 0.37

4p + 3(0.03) = 0.37

4p + 0.09 = 0.37

Subtract 0.09 in both sides:

4p = 0.37 - 0.09

4p = 0.28

Divide both sides by 4:

4p/4 = 0.28/4

p = 0.07

Lets verify our result, replacing p and e found in equation 2:

3(0.07) + 4(0.03) = 0.21 + 0.12 = 0.33

Verified!

a

step-by-step explanation: