Question 60783: Please help. This is for G.E.D. Evaluative Test, Mathematics part 1. I am terrible with word problems.
Ben scored 7 more points than Jack in a basketball game. Paul scored 2 points less than Jack in the same game. If the three boys scored a total of 38 points, how many points did Jack score?
Found 2 solutions by ankor@dixie-net.com, mszlmb:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Ben scored 7 more points than Jack in a basketball game. Paul scored 2 points less than Jack in the same game. If the three boys scored a total of 38 points, how many points did Jack score?
:
It's not that bad, write a simple equation for each statememt:
we agree that:
:
B + P + J = 38
:
"Ben scored 7 more points than Jack "
B = J + 7
:
"Paul scored 2 points less than Jack"
P = J - 2
:
In the original equation B + P + J = 38, we can substitute (J+7) for B & (J-2) for P:
(J+7) + (J-2) + J = 38
J + 7 + J - 2 + J = 38
3J + 5 = 38
3J = 38 - 5
J = 33/3
J = 11 points which is what they asked for.
:
It's an easy matter to find the scores of the others and it's a good idea to do that to check the solution.
18 + 9 + 11 = 38
Answer by mszlmb(115)  (Show Source):
You can put this solution on YOUR website! Ben is B Jack is J Paul is P.
"Ben scored 7 more points than Jack in a basketball game."
B=J+7
"Paul scored 2 points less than jack in the same game."
P=J-2
"If the three boys scored a total of 38 points.."
P+J+B=38
There, we have the equations we need. Take the second:
P-2=J and do plus 2 to both sides, it yields p=J+2.
Since we know that B is J+7 and P is J-2, we can replace B and P in equation 3 with (J+7) and (J-2), respectively.
Equation 3 yields
P+B+J=38
After replacement, it yields:
(J-2)+(J+7)+J=38 which is equivalent to
J-2+J+7+J=38 Combine like terms:
3J+5=38 now do minus 5 to both sides
3J=33 divide all by 3
J=11
And the rest is just substitution; using the first equation:
B=J+7 since J=11, substitute:
B=11+7=18 And thus Ben scored 18 points.
Now do the same with the second:
P=J-2 since J=11
P=11-2=9 And thus Paul scored nine points.
Thence Jack scored 11, Ben scored 18, and Paul scored 9.
Doublecheck!
"Ben scored 7 more points than Jack in a basketball game."
18 is 7 more than 11.
"Paul scored 2 points less than Jack in the same game."
9 is 2 less than 11.
"If the three boys scored a total of 38 points.."
11+18+9=38.
We're good!
Questions or else im or email.
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