Question 60783
Ben is B Jack is J Paul is P.<br>

"Ben scored 7 more points than Jack in a basketball game."
B=J+7<br>

"Paul scored 2 points less than jack in the same game."
P=J-2<br>

"If the three boys scored a total of 38 points.."
P+J+B=38<br>

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.<br>

Since we know that <font color=green>B</font> is <font color=green>J+7</font> and <font color=blue>P</font> is <font color=blue>J-2</font>, we can replace <font color=green>B</font> and <font color=blue>P</font> in equation 3 with (<font color=green>J+7</font>) and (<font color=blue>J-2</font>), respectively.<br>

Equation 3 yields 
<font color=blue>P</font>+<font color=green>B</font>+J=38<br>

After replacement, it yields:
(<font color=blue>J-2</font>)+(<font color=green>J+7</font>)+J=38  which is equivalent to
<font color=blue>J-2</font>+<font color=green>J+7</font>+J=38  Combine like terms:
3J+5=38  now do minus 5 to both sides
3J=33  divide all by 3
J=11<br>

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.<br>

Now do the same with the second:
P=J-2  since J=11
P=11-2=9  And thus Paul scored nine points.<br>

Thence Jack scored 11, Ben scored 18, and Paul scored 9.<br><center><font color=orange><strong><b>Doublecheck!</b></strong></font></center><hr color=blue width=110><br>

"Ben scored 7 more points than Jack in a basketball game."
18 is 7 more than 11.<br>

"Paul scored 2 points less than Jack in the same game."
9 is 2 less than 11.<br>

"If the three boys scored a total of 38 points.."
11+18+9=38.<br>

We're good!<br><br><br>


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