So,
Let x represent Joe's weight and y represent Jeff's weight.
"Joe weighs 20 lbs. less than twice Jeff's weight."
x = 2y - 20
"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
(y + 10) + x = 250
We now have our two open sentences.
x = 2y - 20
(y + 10) + x = 250
Get rid of parentheses.
x = 2y - 20
x + y + 10 = 250
We will use Elimination by Substitution.
2y - 20 + y + 10 = 250
Collect Like Terms.
3y - 10 = 250
Add 10 to both sides.
3y = 260
Divide both sides by 3.
\(Jeff's\ weight = 86 \frac{2}{3} \ lbs.\)
Substitute again.
\(x = 2(86 \frac{2}{3} )-20\)
Multiply.
\(x = 173 \frac{1}{3} -20\)
Subtract.
\(Joe's\ weight = 153 \frac{1}{3}\ lbs.\)
Check.
"Joe weighs 20 lbs. less than twice Jeff's weight."
Jeff's weight times two is 173 and one-third.
20 lbs. less than that is 153 and one-third lbs. Check.
"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
86 and two-thirds + 10 = 96 and two-thirds.
96 and two-thirds + 153 and one-third equals 250 lbs. Check.
\(Joe's\ weight\ is\ 153 \frac{1}{3} \ lbs.\)
\(Jeff's\ weight\ is\ 86 \frac{2}{3} \ lbs.\)
