SOLUTION: I noticed this question # 1105910 is exactly like mine with one exception. My text only gives the first part about the woman's investment and that's where I'm stuck.
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Question 1159066: I noticed this question # 1105910 is exactly like mine with one exception. My text only gives the first part about the woman's investment and that's where I'm stuck.
The text reads: "A woman has two investments, one paying a 6% dividend. The other is $680 more than half the first and pays a 5% dividend. If the total return is $102, find the investments." The text suggests 0.06x + 0.05y=102 and
y=680 + x/2. I get stuck using these two equations with the substitution method or by linear combination as the text suggests. The answer you gave to question no. 1105910 had that second part mixed in which confused me since my text doesn't have that. Can you help me in solving the problem my text gave above? Thank you. Found 2 solutions by ikleyn, MathTherapy:Answer by ikleyn(52884) (Show Source):
"A woman has two investments, one paying a 6% dividend. The other is $680 more than half the first and pays a 5% dividend.
If the total return is $102, find the investments."
I will solve it now.
Let x be the amount invested at 6%.
Then the other investment is dollars.
The equation for the total return is
0.06*x + = 102 dollars.
Start multiplying both sides by 2. You will get
0.12x + 0.05*(x+1360) = 204.
From this equation
x = = 800.
ANSWER. First investment (at 6%) is $800. The second investment is = 400+680 = 1080 dollars.
CHECK. 0.06*800 + 0.05*1080 = 102 dollars. ! Correct !
Completed and solved.
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I noticed this question # 1105910 is exactly like mine with one exception. My text only gives the first part about the woman's investment and that's where I'm stuck.
The text reads: "A woman has two investments, one paying a 6% dividend. The other is $680 more than half the first and pays a 5% dividend. If the total return is $102, find the investments." The text suggests 0.06x + 0.05y=102 and
y=680 + x/2. I get stuck using these two equations with the substitution method or by linear combination as the text suggests. The answer you gave to question no. 1105910 had that second part mixed in which confused me since my text doesn't have that. Can you help me in solving the problem my text gave above? Thank you.
Suggested equations: .06x + .05y = 102 ----- eq (i) --------- eq (ii)
Now, just substitute for y in eq (i) to get:
Solve that for x, the amount invested at 6%.
If you want the 5% investment-amount, I do believe that you can find that!
