suppose walmart stok is selling at 59 dollars a share and mattel stock is selling at 28 a share. amy waller has a maximum of 6000 dollars to invest. she wishes to purchase four times as many shares of walmart as of mattel. only whole shares of stock can be purchase. a. how many shares of each will she purchase? how much money will be left over?
number of mattel shares -- x
number of Walmart shares --- 4x
59(4x) + 28x < 6000
264x < 6000
x < 22.7
Since x must be a whole number
x = 22
so 22 Mattel shares and 88 Walmart shares
So how much is left of the 6000 ?
To determine how many shares of each stock Amy Waller will purchase and how much money will be left over, we can follow these steps:
Step 1: Calculate the number of shares for each stock.
Let's assume Amy purchases x shares of Mattel stock.
According to the given information, she purchases four times as many shares of Walmart as Mattel, so she purchases 4x shares of Walmart stock.
Step 2: Calculate the total cost for each stock.
The cost of each share for Walmart stock is $59, and the cost of each share for Mattel stock is $28.
So, the total cost of Walmart stock will be the cost per share ($59) multiplied by the number of shares (4x):
Total cost of Walmart stock = 4x * $59 = $236x
Similarly, the total cost of Mattel stock will be the cost per share ($28) multiplied by the number of shares (x):
Total cost of Mattel stock = x * $28 = $28x
Step 3: Calculate the total amount spent on both stocks.
The total amount spent will be the sum of the total cost for Walmart stock and the total cost for Mattel stock:
Total amount spent = Total cost of Walmart stock + Total cost of Mattel stock
= $236x + $28x
= $264x
Step 4: Determine the maximum amount Amy can invest.
According to the given information, Amy has a maximum of $6000 to invest.
Step 5: Calculate the number of shares based on the maximum investment amount.
To calculate the number of shares Amy can purchase, we need to equate the total amount spent to the maximum investment amount:
$264x = $6000
Step 6: Solve for x.
Divide both sides of the equation by $264:
x = $6000 / $264
Use a calculator to find the value of x:
x ≈ 22.73
Since we can only purchase whole shares, we round down the value of x to the nearest whole number.
So, Amy can purchase 22 shares of Mattel stock.
Step 7: Calculate the number of shares for Walmart stock.
As we know, Amy purchases four times as many shares of Walmart as Mattel.
Therefore, the number of shares for Walmart stock will be 4 times the number of shares for Mattel stock:
Number of shares of Walmart stock = 4 * 22
= 88 shares
Step 8: Calculate the remaining money.
To find out how much money will be left over, subtract the total amount spent from the maximum investment amount:
Remaining money = Maximum investment amount - Total amount spent
= $6000 - $264x
Substituting the value of x:
Remaining money = $6000 - $264 * 22
= $6000 - $5808
= $192
So, Amy will purchase 22 shares of Mattel stock, 88 shares of Walmart stock, and will have $192 left over.