Question

Bill weighs 120 lbs and is gaining ten lbs each month. Phil weighs 150 lbs and is gaining four lbs each month. How many months will it take for bill to wiegh the same as phil?

Answer 1

First, let's write two expressions, letting x= the number of months which have elapsed:

Bill: 120 + 10x
Phil: 150 + 4x

If we set them equal to each other, then solve for x, that will be the number of months where their weights equal each other:

120+10x = 150 + 4x   [starting equation]
-120  -4x    -120 -4x    [ subtract 120 from both sides, and 4x from both sides, to isolate the term with the variable]

6x = 30     [divide both sides by 5]
 5      5

x=6. They will weigh the same in six months.

Answer 2

Algebraic equations are equations that contain variables that are unknown. These unknown variables are represented by any letters of the Alphabet.

it will take 5 months for Bill to weigh the same as Phil.

Let's represent the number of months they gain extra weight as: m

Step 1

Bill weighs 120 lbs and is gaining ten lbs each month. The algebraic equation for the above statement is :

120 ib  + 10 ib x m

120 + 10m ........Equation 1

Phil weighs 150 lbs and is gaining four lbs each month. The algebraic equation for the above statement is :

150 ib  + 4 ib x m

150 + 4m ........Equation 2

Step 2

We equate equations 1 and 2 to each other

Equation 1 = Equation 2

120 + 10m = 150 + 4m

Collect like terms

10m - 4m = 150 - 120

6m = 30

Divide both sides by 6

6m/6 = 30/6

m = 5

Therefore, it will take 5 months for Bill to weigh the same as Phil

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