Question

The value of your EFG stock is three times the value of your PQR stock. If the total value of the stocks is \(\$ 4500,\) how much is invested in each company?

Short answer

The amount invested in PQR is \$1125 and the amount invested in EFG is \$3375.

Step-by-step solution

Formulate the Equations

According to the problem, the total value of EFG and PQR stocks is a total of 4500 dollars. We're also told that the value of EFG is three times the value of PQR. This allows us to form two equations. Let EFG be denoted as x and PQR as y. The equations would be: Equation 1: \(x = 3y\)Equation 2: \(x + y = 4500\)

Substitute Equation 1 into Equation 2

Replace x in equation 2 with 3y from equation 1:\(3y + y = 4500\)Simplify this equation to get the value of y (PQR stock).

Solve for PQR

Solve the equation from the step 2:\(4y = 4500\)Divide by 4 on both sides:\(y = \frac{4500}{4} = 1125\)So, \$1125 is invested in PQR.

Solve for EFG

Substitute y = 1125 into equation 1:\(x = 3\cdot 1125 = 3375\)So, \$ 3375 is invested in EFG.