Word Problem Question

Question

At a toy store, 4 toy cars were sold at $15 and 3 teddy bears were sold at #20. Tim only bought toy cars and Justin only bought teddy bears from the store. They spent the same amount of money but Tim had 49 more items than Justin. How much money did each of them spend?

Answer 1

Hi Carla,

The key to word problems is identifying the information given and exactly what the question is looking for you to find.

Your Question: At a toy store, 4 toy cars were sold at $15 and 3 teddy bears were sold at #20. Tim only bought toy cars and Justin only bought teddy bears from the store. They spent the same amount of money but Tim had 49 more items than Justin. How much money did each of them spend?

Given:

4 cars cost $15 (unit price per car would be $15/4)

3 bears cost $20 (unit price per bear would be $20/3)

Tim only bought cars

Justin only bought bears

Tim and Justin spend the same amount of money

Tim had 49 more items than Justin

Find: How much money did they each spend

Let

c=number of cars bought

b=number of bears bought

NOTE: We have 2 unknowns above, that means we need at least 2 equations to solve the problem.

Cost for Tim's cars would be the number of cars purchased times the unit price (he only bought cars)

Tim Cost = c ($15/4)

Justin cost = b ($20/3) (Justin only bought bears)

They spend the same amount of money. This means that their costs are equal, so we can set these equations equal to each other.

c(15/4) = b(20/3) - This is our first equation.

Now we use the fact that Tim had 49 more items than Justin to generate a 2nd equation

cars = bears + 49 Tim's items equal Justin's plus 49

c=b+49

Now you have 2 equations you can solve.

c=b+49 and c(15/4) = b(20/3)

c(15/4) = b(20/3)

(b+49)(15/4) = b(20/3)

(15/4)b+(735)/4 = b(20/3)

(15/4 -20/3)b = - 735/4

((45 -80)/12)b = -735/4

(-35/12)b = -735/4

b = 63 This is the number of bears sold

c = 63+49 = 112 This is the number of cars sold.

We need to find how much each person spend.

Tim Cost = c ($15/4)

Tim cost = 112($15/4) = $420

Justin cost = b ($20/3)

Justin cost = 63(20/3) = $420

We know from above that the costs should be the same and they are.

Hope this helps!!

Let me know if you have more questions :)