Question 1154337
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Ans:
Say Mark invested x dollars.
Then Sarah invested (x - 1000) dollars
Interest earned by Mark = {{{x * 0.09}}}
Interest earned by Sarah = {{{(x - 1000) * 0.05}}} = {{{0.05x - 50}}}
Total interest = 790
So we have the equation
{{{0.09x + 0.05x - 50 = 790}}}
Moving constants to one side and variables to the other side

{{{0.14x = 840}}} or {{{x = 6000}}}

So Mark invested 6000 dollars and Sarah invested (6000 - 1000) = 5000 dollars.

Check
Interest for Mark = {{{6000 * 0.09 = 540}}}

Interest for Sarah = {{{5000 * 0.05 = 250}}}

Total interest = {{{540 + 250 = 790}}} Check successful!

<b>Ans: Mark = $6000, Sarah = $5000</b>

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