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?
<pre><b>1.</b>
Let rate be r
The we get: .06(300) + r(400) > 70
18 + 400r > 70
400r > 52
Rate, or {{{highlight_green(matrix(1,15, r, MUST, be, ">", 52/400, ",", or, r, MUST, "be", ">", ".13,", or, ">", "13%"))}}}
<b>2.</b>
Let number she bought be G
Cost of each ball: {{{5/G}}}
Had each cost 25c less, then each would be {{{5/G - .25}}}
We then get: {{{matrix(1,3, (5/G - .25)(G + 1), "=", 5)}}}
{{{matrix(1,3, 5 + 5/G - .25G - .25, "=", 5)}}} ------ FOILing binomials on left side
{{{matrix(1,3, 5/G - .25G - .25, "=", 0)}}}
{{{matrix(1,3, 5 - .25G^2 - .25G, "=", 0)}}} ------- Multiplying by LCD, G
{{{matrix(1,3, - .25G^2 - .25G + 5, "=", 0)}}}
{{{matrix(1,3, G^2 + G - 20, "=", 0)}}} ------- Multiplying by - 4 to clear DECIMALS
(G - 4)(G + 5) = 0 --- Factoring TRINOMIAL on left side
Number of golf balls purchased, or {{{highlight_green(matrix(1,3, G, "=", 4))}}}       OR        G = - 5 (ignore)