SOLUTION: seven pencil and five eraser costs $11.60, whereas 5 pencil and 3 eraser cost $7.60. calculate the cost of 8 erasers.

Question 23546: seven pencil and five eraser costs $11.60, whereas 5 pencil and 3 eraser cost $7.60. calculate the cost of 8 erasers.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
7p+5e = 11.60
5p +3e = 7.60

I recommend the elimination (addition) method. To eliminate the e variable, the common number between the coefficients is 15 (like an LCD!). To get a 15 in the first equation, multiply both sides by 3. To get a -15 in the second equation and make the variable subtract out, multiply the second equation by -5.

3(7p+5e) = 3(11.60)
-5(5p +3e) =-5( 7.60)

21p + 15e = 34.80
-25p -15e = -38.00

Add the two equations together:
-4p = -3.20

Divide both sides by -4:

p= $.80

Substitute p into the first equation and solve for e:
7p+5e = 11.60
7(.80) + 5e=11.60
5.60 + 5e = 11.60

Subtract 5.60 from each side:
5.60-5.60 +5e= 11.60-5.60
5e = 6.00

e = $1.20

Check in second equation:
5p+3e= 7.60
5(.80)+3(1.20)= 7.60
4.00 + 3.60 = 7.60
It checks!!

Now, the LAST step in any word problem is to ANSWER THE QUESTION!
Cost of 8 erasers = 8(1.20) =$9.60 (plus tax!!)

R^2 at SCC
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