A garden table and a bench cost $600 combined. The cost of the garden table is three times the cost of the bench. What is the cost of the bench?

Question

 A garden table and a bench cost $600 combined. The cost of the garden table is three times the cost of the bench. What is the cost of the bench?

Answer 1

So, your initial equation will represent the problem as follows:

Cost of table + cost of bench = 650 dollars

You will modify your equation to represent the cost of the table as a function of the bench.

The table costs 3 times as much as the bench.

So,

T + B = 600

3B + B = 600                  Set up modified equation

4B = 600                        Add like terms

B = 150                          Divide each side by 4

Check:

3 * 150 + 150 = 600

450 + 150 = 600

600 = 600

Table cost = 450 dollars

Bench cost = 150 dollars

Total Cost (T + B) = 600 dollars

Answer 2

If the bench=x, then the garden table=3x. Therefore, the entire equation will read 3x + x = $600. We combine like terms, so 4x = $600. Then we have to get x by itself so we divide both sides by 4 which looks like this 4x/4 = $600/4.

Leaving x = $150. Going back to the original question, it states that the garden table is three times the cost of the bench. At the beginning we identified the bench=x and the garden table=3x. Therefore, the bench is $150 and the garden table is $450.

Answer 3

2 equations, 2 unknowns.

 

let g= cost of garden table and b=cost of bench.

 

g + b =600

 

g = 3b

 

I'll use substitution to solve this system of equations.  Replace g with 3b in first equation.

 

3b + b = 600 >>>  4b = 600 >>> b=150.

 

so g = 3 *150  g=450.