Question

Anna inherits $70000 and decides to invest part of it in an education account for her daughter and the rest in a 5 year CD. If the amount she puts in the education account is $10000 more than three times the amount she puts in the CD, how much money does Anna invest in each account?

Answer 1

E = amount she put for Education

CD = amount she put for a Certificate of Deposit.

so, whatever those amounts are, we know that all she got is 70,000 bucks total, so E + CD = 70000.

how much is three times the CD?  well, 3*CD or 3CD.

how much is 10,000 more than that?  well 3CD + 10000.

since we know that the amount on Education was 10000 more than three times the CD, then E = 3CD + 10000.

$\bf \begin{cases} E+CD=70000\implies \boxed{CD}=70000-E\\ E=3CD+10000\\ ------------------\\ E=3\left( \boxed{70000-E}\right)+10000 \end{cases} \\\\\\ E=210000-3E+10000\implies 4E=200000\implies E=\cfrac{200000}{4} \\\\\\ E=50000$

how much was it invested in the CD?  well, CD = 70000 - E.

Answer 2

You want 3 times the cd, so 3x. Then 10000 more so +10000. Your total is 70000.

$3x+10000+x=70000 \\ \\ 4x+10000=70000 \\ \\ 4x+10000-10000=70000-10000 \\ \\ 4x=60000 \\ \\ \frac{4x}{4} =\frac{60000}{4} \\ \\ x=15000 \\ \\ 15000+3(15000)+10000=70000 \\ \\ 15000+45000+10000=70000 \\ \\ 15000+55000=70000 \\ \\ 70000=70000$

So the CD is $15,000
Education = 70000 - 15000
Education = $55,000