How to do this problem?

Question

As an incentive to get his son to do his arithmatic homework, a father offered him 10 cents for every problem done correctly but fined him 6 cents for every problem done incorrectly. When the father corrected the 24 problems, neither owed any money to the other. How many problems did the boy solve correctly?

I know that the right answer is 9 problems, but i need an actual EXPLANATION, not just a formula...

by the way terry, this is for an entrance exam my own homework is 100x easier...

Answer 1

let x = the number correct
therefore, 24-x = number incorrect
he earns $+.10, but loses so $-.06

$0 = .10x + -.06(24-x)
0 = .10x + - 1.44 + .06x
0 = .16x - 1.44
1.44 = .16x
x = 9

Answer 2

I am assuming that you know basic algebra, involving systems of equations. If not, then I would advise you to go to http://www.phschool.com/webcodes10/index.cfm?fuseaction=home.gotoWebCode&wcprefix=ate&wcsuffix=0702

I have personally found their homework video tutors very helpful.

Now, once you have that mastered, we will return to the problem. Let's restate this problem in terms that we can use for an equation:

For each problem done correctly, 10 is gained. For each problem done incorrectly, 6 is lost.

Let's say that the number of problems done correctly is X, and the problems done incorrectly is Y.

Therefore:

10x - 6y = 0.

10 times the the number of correct problems (X) minus 6 times the number of incorrect problems (Y) is zero, as the problem states. We subtract the 6y because this is the money lost.

Now, where does the 24 problems come in? That is where we need to use a system. You see, the number of correct and incorrect problems must add up to 24, as there are only 24 problems. This is quite simply transformed into an equation:

x + y = 24.

So we have two equations now:

10x - 6y = 0
x + y = 24

How do we extract an answer from this? Well, what we have to do is move around the terms in one of the equations until we get the variables alone on one side. Then, we can substitute what that variable equals in the other equation. Since the second equation has no coefficients for the variables, it would simpler to get by itself. So we have the second equation:

x + y = 24
x = 24 - y

So now we know what X equals in terms of Y. We can substitue that in the other equation:

10(24 - y) - 6y = 0
240 - 10y - 6y = 0
240 - 16y = 0
-16y = -240
y = 15

Now we can substitue this value of Y in the second equation:

x + y = 24
x + 15 = 24
x = 9

So X equals 9, and Y equals 15. The boy got 9 problems correct and 15 incorrect.

Hope that helps!

Answer 3

9

Answer 4

let x be the amount of answers anwered correctly, and y be the number of incorrect answers.

10x-6y=0, since neither dad nor son got anything
x+y=24, since the total number of problems equals no, answered correctly plus incorrect answer no.

time x+y=24 by 10, making it 10x+10y=240. subtract 10x+10y=240 from 10x-6y=0, and u get -16y=-240, simplify it out in order to get y=15. Now put y=15 back into the equation x+y=24, and u get x=9. Thus, 9 correct answers is the answer :) yay! problem solved!

Answer 5

I'm interpreting "the father corrected 24 problems" to mean that he reviewed 24 problems (and not 24 problems incorrectly done):

if X is the number of correct answers and Y is the number of incorrect answer then
10X = 6Y
and
X+Y=24

so Y=24-X then by substituting
10X = 6 (24-X) and solve for X will give you the answer.

Answer 6

Let x represent the number solved correctly.
Then 24-x is the number solved incorrectly.
10x = 6(24-x)
10x = 144-6x
16x = 144
x = 144/16 = 9
9 correct answers

Answer 7

The boy solved 9 problems correctly

Answer 8

the son did 15 problems incorrectly and 9 problems correctly
i=incorrect problems
c=correct problems
i+c=24 10c=6i
c=24-i 10(24-i)=6i
240-10i=6i
240=16i
15=i

Answer 9

Please consider getting a tutor. The tutor can present problems in ways that are different than your teacher's, and between the two may make it easy to understand.

0.10X = 0.06(24-X)

solve for X (number of correct problems for which Dad paid 10 cents each.)

0.10X = 1.44 - 0.06X

0.16X = 1.44

X = 1.44/0.16

X = 9

Answer 10

Let x = problems correct
then 24 - x problems wrong

then

0.10x = (24 - x)0.06

0.10x = 1.44 - 0.06x

0.16 x = 1.44

x = 9 correct problems
.