Question

a garden table and a bench cost $613 combined. the garden table cost $87 less then the bench. what is the cost of the bench ?

Answer 1

the cost of the bench is 350

Step-by-step explanation

Step 1

let

x represents the cost of the garden table

y represents the cost of the bench

so

a)a garden table and a bench cost $613 combined.

`x+y=613\rightarrow equation\text{ (1)}`

b)the garden table cost $87 less then the bench,( in other words, you have to add 87 to the price of the garden table to obtain the cost of the bech)

`\begin{gathered} x+87=y\rightarrow Equation(2) \\ \end{gathered}`

Step 2

solve the equations

a)isolate x in equaiton (1) and replace in equation (2)

`\begin{gathered} x+y=613\rightarrow equation\text{ (1)} \\ \text{subtrac y in both sides} \\ x+y-y=613-y \\ x=613-y \end{gathered}`

now, replace in equation (2)

`\begin{gathered} x+87=y\rightarrow Equation(2) \\ (613-y)+87=y\rightarrow Equation(2) \\ 700-y=y \\ \text{add y in both sides} \\ 700-y+y=y+y \\ 700=2y \\ \text{divide both sides by 2} \\ (700)/(2)=(2y)/(2) \\ 350=y \end{gathered}`

it means, the cost of the bench is 350