Use at least two different methods to find the time in weeks when moe and larry will have the same amount of money in savings account

Question

Moe and larry each need to raise $200. Moe has $35 in savings and earns $20 per week. Larry has $60 in savings and receives $10 per week. Use at least two different methods to find the time in weeks when moe and larry will have the same amount of money in savings account

Answer 1

First, assign variables to the amount of money that each will have so we can set it equal at 200:

     M=amount of money Moe has

     L=amount of money Larry has

     W=number of weeks

 

Then, describe M and L:

     M = 35 + 20W                [$35 savings + $20/wk)times weeks]

      L =  60 + 10W

 

The problem asks us to find W when Moe and Larry have the same amount, so set M=L and solve for W:

       35 + 20W = 60 +10W

               10W = 25        (subtract 10W+35 from both sides)

                 W = 2.5         (divide both sides by 10)

Answer: 2.5 weeks; but if they receive a weekly allowance, we need a whole week, so W=3.

 

Now, you probably have studied another method for solving this, so use it.

 

I’m going to describe how much more money Larry has than Moe (because he starts with $60 versus $35 in savings) and determine how many weeks it takes for that lead to become 0.

     Lead = [ 60 + 10W ] - [ 35 + 20W ]

         0    =  25 - 10W       (collect terms)

         -25 = -10W           (subtract 25 from both sides)

          2.5 = W               (divide both sides by -10)

         W=3             (round up because we need whole weeks)

 

Checking (very important):

   Is  60+10(2.5) = 35 + 20(2.5)    ?

           60+25   =  35 + 50   ?

                85 = 85   ?  yes