Question

suppose nike stock is selling at $76 a share and kellogg stock is selling at $33 a share. mike moussa has a maximum of $10,000 to invest. he wishes to purchase five times as many shares of kellogg as of nike. only whole - shares of stock can be purchased.
a) how many shares of each will he purchase?
b) how much money will be left over?
a) he will purchase shares of nike and shares of kellogg.
(type whole numbers.)

Explanation:

Step1: Define variables

Let $x$ be the number of Nike - shares. Then the number of Kellogg - shares is $5x$.

Step2: Set up the cost equation

The cost of Nike shares is $76x$ and the cost of Kellogg shares is $33\times5x = 165x$. The total cost $C=76x + 165x=241x$. The total amount of money available for investment is $10000$. So we have the inequality $241x\leq10000$.

Step3: Solve for $x$

$x=\lfloor\frac{10000}{241}
floor$. Calculate $\frac{10000}{241}\approx41.49$. Since $x$ must be a whole number, $x = 41$.

Step4: Find the number of Kellogg shares

The number of Kellogg shares is $5x$. Substitute $x = 41$ into $5x$, we get $5\times41 = 205$.

Step5: Calculate the total cost of the shares

The total cost of the shares is $76\times41+33\times205=3116 + 6765=9881$.

Step6: Calculate the money left - over

The money left - over is $10000−9881 = 119$.

Answer:

a) He will purchase 41 shares of Nike and 205 shares of Kellogg.
b) $119$