Question 541266
Here you are solving for 3 different variables. I'd suggest solving for 1 variable and substituting back in to the problem. Let's start with turning the words into equations:
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"Roger, Sue, and Tim have $155 among them."
1) {{{r+s+t=155}}}
"Roger has $5 more than Sue and Tim together."
2) {{{r=s+t+5}}}
"If Sue gives Time $5 he will have twice as much as she does."
3) {{{2*(s-5)=(t+5)}}}
"How much does each have?"
Now it's time to solve.
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The way to substitute, is to say either r= or s= or t= something, and replace a variable with that "something" in another problem. Fortunately, equation 2 already has {{{r=s+t+5}}}, so that's where we'll start. Plug that back into #1 in place of R.
1){{{r+s+t=155}}} becomes
{{{(s+t+5)+s+t=155}}}
{{{2s+2t=150}}}
{{{s+t=75}}}
And we can't really reduce further.
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Let's also make #3 easier to read.
3) {{{2*(s-5)=t+5}}}
{{{2s-10=t+5}}}
{{{t=2s-15}}}
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Now we know what T "equals" so we can plug that into our simplifed #1 and solve for S.
1) {{{s+t=75}}} becomes
{{{s+(2s-15)=75}}}
{{{3s-15=75}}}
{{{3s=90}}}
{{{s=30}}}
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Now that we know what S equals, we can easily solve for R and T. Plug 30 in for S in the following equation.
3) {{{t=2s-15}}}
Once you figure out what T is, you can solve
2) {{{r=s+t+5}}}
and you can check your answer with
1) {{{r+s+t=155}}}
Hope this helps!