SOLUTION: 1. George has $700 to invest. Suppose he invests $300 at 6% interest. At what rate must he invest the other $400 so that the two investments yield more than $70 of yearly interest?

Algebra.Com
Question 1137893: 1. George has $700 to invest. Suppose he invests $300 at 6% interest. At what rate must he invest the other $400 so that the two investments yield more than $70 of yearly interest?

2. Angie bought some golf balls for $5. If each ball had cost $0.25 less, she could have purchased one more ball for the same amount of money. How many balls did Angie buy?
Found 2 solutions by VFBundy, MathTherapy:
Answer by VFBundy(438)   (Show Source): You can put this solution on YOUR website!
1. George has $700 to invest. Suppose he invests $300 at 6% interest. At what rate must he invest the other $400 so that the two investments yield more than $70 of yearly interest?

6% interest rate:
Principal = 300
Rate = 0.06
Interest = 300 * 0.06 = 18

Other interest rate:
Principal = 400
Rate = 52/400 = 0.13
Interest = 70 - 18 = 52

To yield MORE than $70 worth of interest, the $400 must be invested at a rate HIGHER than 13%.

2. Angie bought some golf balls for $5. If each ball had cost $0.25 less, she could have purchased one more ball for the same amount of money. How many balls did Angie buy?

c = cost of each ball
n = number of balls

c * n = 5
(c - 0.25) * (n + 1) = 5

This means:
c * n = (c - 0.25) * (n + 1)

Simplify:
cn = cn - 0.25n + c - 0.25

Solve for c:
0 = c - 0.25n - 0.25

c = 0.25n + 0.25

From earlier, we know:
c * n = 5

Substitute 0.25n + 0.25 for c:
c * n = 5

(0.25n + 0.25) * n = 5

Solve for n:
0.25n² + 0.25n = 5

0.25n² + 0.25n - 5 = 0

Use quadratic formula.


You will find that n = 4 and n = -5. Since the number of balls purchased cannot be a negative number, you can throw out n = -5. We are left with n = 4.

We now know Angie bought 4 balls.

From earlier:
c * n = 5

Substitute '4' for n:
c * 4 = 5

Solving for c, we find that c = 1.25.

In summary, Angie bought four balls at $1.25 apiece. (Had each ball been $0.25 cheaper, she could've bought five balls at $1.00 apiece.)
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
1. George has $700 to invest. Suppose he invests $300 at 6% interest. At what rate must he invest the other $400 so that the two investments yield more than $70 of yearly interest?

2. Angie bought some golf balls for $5. If each ball had cost $0.25 less, she could have purchased one more ball for the same amount of money. How many balls did Angie buy?
1.

Let rate be r

The we get: .06(300) + r(400) > 70

18 + 400r > 70

400r > 52

Rate, or 

2.

Let number she bought be G

Cost of each ball: 

Had each cost 25c less, then each would be 

We then get: 

 ------ FOILing binomials on left side



 ------- Multiplying by LCD, G



 ------- Multiplying by - 4 to clear DECIMALS

(G - 4)(G + 5) = 0 --- Factoring TRINOMIAL on left side

Number of golf balls purchased, or        OR        G = - 5 (ignore) 

RELATED QUESTIONS


Marcia has $18000 to invest in two different investments. She invest $10000 at 4% yearly... (answered by josmiceli)

Mr. Jones has $10,000 to invest. He invests part at 6% and the rest at 8%. If he earns... (answered by ikleyn)

Mr Jones has $10,000 to invest. He invests part at 6% and the rest at 8%. If he earns... (answered by ikleyn)

Joey has S500,000. If he invest at S300000 at 9% interest at what rate must he invest the  (answered by mathmate,MathTherapy)

Mr. Jones has $25,000 to invest. he invests part at 8% and the rest at 9%. if he earns... (answered by ikleyn)

Mr. Jones has $16,000 to invest. He invests part at 9% and the rest at 10%. If he earns... (answered by mananth,ramkikk66)

Bradley has $25,000 that he wants to invest. He invests it in accounts paying 12%, 7%,... (answered by ewatrrr)

Marcia has $18,000 to invest in two different investment.  she invested $10,000 at 4%... (answered by ikleyn)

nico is saving money for his college education he invests some money at 7% and $2200 less  (answered by richwmiller)