A garden table and a bend cost $842 combined. The garden table costs $58 less than the bench. What is the cost of the bench ?

Answer 1

For those who can solve a problem (equation) with one variable, a two-variable equation is a pretty easy step from there.

Let's let the cost of the Table be T. The cost of the Bench is B.

We are told that the two items together cost $842. This becomes the equation T + B = 842.

We are also told that the Table costs $58 less than the Bench. This becomes the equation T = B - 58.

We are being asked the cost of the Bench (B). We can take either of our two equations and rework them into a form that reads B = ___.

Let's take the first one:

T + B = 842

Subtract T from both sides. (An equation will still be true if we do the same operation to both sides).

T + B - T = 842 - T

But since T - T = 0, the equation becomes

B = 842 - T

In order to determine B, we need to "get rid of" that T. We can use the other equation to accomplish that, and put it in the form of T = ___. In fact, it already is: T = B - 58

Now we can substitute this value of T into the first equation, which you remember has become:

B = 842 - T

B = 842 - (B - 58)

or

B = 842 - B + 58

or

B = 900 - B

To "get rid of" the B on the left side, and to end up with an equation which says what B equals, we need to add B to both sides:

B + B = 900 - B + B

or

2B = 900

Divide both sides by 2 to come down to:

2B/2 = 900/2

B = 450. The bench costs $450.

(And by the way, we also know that T = B - 58, or T = $392. So we also know the cost of the table).

If we have time, we check our answers into the two original statements to see if they are true. 1) The table and bench costs $842. $450 + $392 = $842. True. 2) The table costs $58 less than the bench. $450 - $392 = $58. True. We've got the right answer.

Answer 2

This is a single variable equation. Let's say the bench costs x dollars. Since the table costs $58 less than the bench, the table costs x - 58 dollars.

Together x + x - 58 they cost $842. So our equation is:

x + x - 58 = 842

Combine the x

2x - 58 = 842

Add 58 to both sides

2x - 58 + 58 = 842 + 58

2x = 900

Divide both sides by 2

2x / 2 = 900 / 2

x = 450

Now that we know what x is we are halfway finished.

We said the the bench costs x. So the bench costs $450.

We said that the table costs x - 58. So the table costs $450 - $58 or $392.

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