Question 1015670: Cadence has $12,000 to invest. She can invest in bonds that pay 10% interest and
CDs that pay 6% interest. She wishes to invest some both ways. How much does she invest in each if she earns $1070 interest in one year? Need equation please.
Found 2 solutions by macston, addingup:
Answer by macston(5194)   (Show Source):
You can put this solution on YOUR website! .
T=amount at 10%; S=amount at 6%
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T+S=$12000
T=$12000-S . Use this to substitute for T below.
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0.10T+0.06S=$1070 . Substitute for T from above.
0.10($12000-S)+0.06S=$1070
$1200-0.10S+0.06S=$1070
-0.04S=-$130
S=$3250
ANSWER 1: She should invest $3250 at 6%.
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T=$12000-S=$12000-$3250=$8750
ANSWER 2: She should invest $8750 at 10%.
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CHECK:
0.10T+0.06S=$1070
0.10($8750)+0.06($3250)=$1070
$875+$195=$1070
$1070=$1070
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Answer by addingup(3677)  (Show Source):
You can put this solution on YOUR website! Some in bonds at 0.10
Some in CDs at 0.06
Total 12,000
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Let's call the investment in bonds x
What's left of the 12,000 she will invest in CDs.
So:
bonds = x
CDs = 12,000-x
Good so far? OK, let's do this:
0.10x+0.06(12,000-x) = 1,070
I will rearrange the terms to make it more intuitive:
0.10x-0.06+720 = 1,070 Subtract x on left and subtract 720 on both sides:
0.04x = 350 Divide both sides by 0.04
x = 8,750 is how much she invested in bonds. And:
12,000-8,750 = 3,250 in CDs
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Check:
8,750*0.10 = 875
3,250*0.06 = 195
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Total... = 1,070 We have the correct answer
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