Question 1189607: Ashley had 24 math problems for her homework. Her father made the following deal with her. He said "I'll give you $5 for every problem you got right, but you pay me $3 for every problem you got wrong." If Ashley broke even on this deal, how many problems did she get correct? Write an equation to solve the problem.
Found 3 solutions by Theo, ankor@dixie-net.com, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number right.
let y = the number wrong.
x + y = 24
5x - 3y = 0
these 2 equations need to be solved simultaneously.
the first equation tells you the total number right and wrong.
the second equation tells you the the scores for the number right and the scores for the number wrong.
multiply both sides of the first equation by 5 and leave the second equation as is to get:
5x + 5y = 120
5x - 3y = 0
subtract the second equation from the first to get 8y = 120
solve for y to get y = 120 / 8 = 15.
this makes x = 9 because 15 + 9 = 24.
5x - 3y becomes 5 * 9 - 3 * 15 which becomes 45 - 45 = 0.
that confirms the values of x and y are good.
the solution is that she got 9 correct and 15 wrong.
the two equations that needs to be solved simultaneously were:
x + y = 24
5x - 3y = 0
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! Ashley had 24 math problems for her homework.
Her father made the following deal with her.
He said "I'll give you $5 for every problem you got right, but you pay me $3 for every problem you got wrong."
If Ashley broke even on this deal, how many problems did she get correct?
Write an equation to solve the problem.
:
let r = no. of problems she got right
then
(24-r) = no. she got wrong
:
5r = 3(24-r)
5r = 72 - 3r
5r + 3r = 72
8r = 72
r = 72/8
r = 9 problems right
:
;
Check this; she got 24 - 9 = 15 problems wrong
5*9 = $45
3*15 = $45
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
It can be solved MENTALLY.
From the condition, for every 3 problems solved correctly, should be 5 problems solved incorrectly.
So, we can divide 24 problems in groups, combining 3+5 = 8 such problems in each group.
The number of groups is 24/8 = 3, which gives the
ANSWER. 3*3 = 9 problems solved correctly and 3*5 = 15 problems solved incorrectly.
Solved (mentally, without using equations).
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I'd recommend Ashley to visit this forum regularly . . .
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