Question

Mary Jo spends $1,980 to buy stock in two companies. She pays $15 a share to one of the companies and $12 a share to the other. If she ends up with a total of 150 shares, how many shares did she buy at $15 a share and how many did she buy at $12 a share?

Answer 1

She bought 60 shares at $15 and 90 shares at $12

Explanation

to solve this we can use a system of equations

so

Step 1

set the equations

let x represents the number of shaper she bougth at $ 15

let x represents the number of shaper she bougth at $12

so

a)Mary Jo spends $1,980 to buy stock in two companies.

$15x+12y=1980\Rightarrow equation(1)$

b)she ends up with a total of 150 shares,so

$x+y=150\Rightarrow\text{ equation\lparen2\rparen}$

Step 2

now, solve the equations

$\begin{gathered} 15x+12y=1980\Rightarrow equation(1) \\ x+y=150\operatorname{\Rightarrow}\text{equat}\imaginaryI\text{on}\operatorname{\lparen}\text{2}\operatorname{\rparen} \end{gathered}$

a) isolate the x value in equation (1) and replace the result in equation(1)

$\begin{gathered} x+y=150\Rightarrow\text{ equation\lparen2\rparen} \\ subtract\text{ y in both sides} \\ x+y-y=150-y \\ x=150-y \end{gathered}$

replace in equation (1) and solve for y

$\begin{gathered} 15x+12y=1980\Rightarrow equation(1) \\ 15(150-y)+12y=1980 \\ 2250-15y+12y=1980 \\ 2250+3y=1980 \\ subtract\text{ 2250 in both sides} \\ 2250+3y-2250=1980-2250 \\ 3y=270 \\ divide\text{ both sides by 3} \\ \frac{3y}{3}=\frac{270}{3} \\ y=90 \end{gathered}$

so,she bougth 90 shares at $12

b) now, replace the y value in equation (2) and solve for x

$\begin{gathered} x+y=150\Rightarrow\text{ equation\lparen2\rparen} \\ x+90=150 \\ subtract\text{ 90 in both sides} \\ x+90-90=150-90 \\ x=60 \end{gathered}$

so, she bougth 60 shares at $15

therefore, the answer is

She bought 60 shares at $15 and 90 shares at $12

I hope this helps you