Question

a couch and coffee table cost 1023. the cost of the couch is 2 times thr cost of the table. what is the cost of both items

Answer 1

Let the cost of the couch be x and the cost of the coffee table be y. If the cost of the couch is 2 times that of the coffee table, then it means the cost of the couch (which is x) is 2 times y. Simply put,

x = 2y.

If both items cost 1023, then it means;

x + y = 1023.

Therefore;

$\begin{gathered} x=2y---(1) \\ x+y=1023---(2) \\ \text{Substitute for x=2y into equation (2)} \\ 2y+y=1023 \\ 3y=1023 \\ \text{Divide both sides by 3} \\ \frac{3y}{3}=\frac{1023}{3} \\ y=341 \\ \text{Substitute for the value of y into equation (1)} \\ x=2(341) \\ x=682 \end{gathered}$

Therefore, the cost of the couch is 682, and the cost of the coffee table is 341.