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?
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?
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.)
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)
