If one table and two lamps cost $88, and two
tables and three lamps cost $153, how much
does a lamp cost?


Sagot :

Answer:

One lamp is equal to 23 dollars

One table is equal to 42 dollars.

Step-by-step explanation:

We can solve this by first organizing what we have.

1 table (t) + 2 lamps (l) = 88.

2 tables (t) + 3 lamps (l) = 153.

_____________

===============

1t + 2l = 88

2t + 3l = 153

===============

-------------------------

If we multiply both sides by 2 on the first equation of

1t + 2l = 88

we could get

2t + 4l = 176.

If that is true, we can subtract the second equation of

2t + 3l = 153 from the new equation to get the price of a lamp.

    2t + 4l = 176

-    2t + 3l = 153

____________

= 0t + l = 23

One lamp is equal to 23.

We can check this by plugging it into an equation.

1 + 2(23) = 88

1t + 46 = 88

1t + 46 - 46 = 88 - 46

1t = 42

If one table equals 42, we can put this back into the second equation to check.

2 (42) + 3 (23) = 153

84 + 69 = 153

That is correct.

Another way to solve is to put this like a system of equations in a graph, by replacing "t" by "x" for example, and "l" by y.

Then you could put it into a graphing calculator and solve by looking for the place where the two lines converge or meet.

Since we put "x" for "t", that means that whatever the x-value is on the solution point, that is the cost of a table, and the y-value is the cost of the lamps.

Another way to solve, is to find the unit rate first by subtracting the first equation from the second equation.

    2t + 3l = 153

 -  1t + 2l = 88

____________

= t + l = 65

If t + l = 65, we can rearrange that equation to be something like t = 65 - l.

That means "t" is equal to 65 bucks minus a lamp.

We put this back into the first equation of

1t + 2l = 88

and replace "t" with the previous expression.

1(65 - l) + 2l = 88

Simplify/distributive property

65 - l + 2l = 88

65 - 65 - l + 2l = 88 - 65

-l + 2l = 23

l = 23

One lamp is equal to 23 bucks.

Confirmed :)

A lamp cost $23

Let the cost of a table be represented by x

Let the cost of a lamp be represented by y.

Since one table and two lamps cost $88, this can be represented as:

x + 2y = 88 ........ equation i

Since two tables and three lamps cost $153, this can be represented as:

2x + 3y = 153 ........ equation ii

Therefore, the equations are:

x + 2y = 88 ....... i

2x + 3y = 153 ....... ii

From equation i,

x + 2y = 88

x = 88 - 2y ...... iii

Put the value of x into equation ii

2x + 3y = 153

2(88 - 2y) + 3y = 153

176 - 4y + 3y = 153

Collect like terms

-4y + 3y = 153 - 176

-y = -23

y = 23

Therefore, a lamp cost $23

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