SOLUTION: Marge purchased x bicycle helmets and y tire pumps. Each helmet cost $15.00 and each pump cost $7.00. She purchased a total of 21 items and spent $243.00. How many helmets did M

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Question 1193922: Marge purchased x bicycle helmets and y tire pumps. Each helmet cost $15.00 and each pump cost $7.00. She purchased a total of 21 items and spent $243.00. How many helmets did Marge buy?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


A setup for solving the problem using formal algebra....

x+y=21 (the total number of items was 21)
15x+7y=243 (the total cost was $243)

With the two equations in that form, I would solve using elimination:

7x+7y=147 (first equation, multiplied by 7)
15x+7y=243
8x=96 (difference between the two equations)

I'll let you finish; it's basic algebra.

An informal solution, using logical reasoning and mental arithmetic (which gives you better mental exercise than using formal algebra....):

The cost of each helmet is $15, which is a multiple of $5; so the total cost of the helmets will be a multiple of $5 -- i.e., the units digit of the total cost of the helmets is either 5 or 0.
Since the total cost of all the items has units digit 3, the total cost of the pumps at $7 each must be either 3 or 8. So the possible numbers of pumps are 4, 9, 14, or 19.

Try each possibility to see which one satisfies all the conditions of the problem.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Marge purchased x bicycle helmets and y tire pumps.
Each helmet cost $15.00 and each pump cost $7.00.
She purchased a total of 21 items and spent $243.00.
How many helmets did Marge buy?
~~~~~~~~~~~~~~~~~~~~~~~ 

Since the problem asks only about helmets, I would solve it using one unknown and one equation,
instead of the system.


Let the number of helmets be x; then the number of tire pumps is (21-x).


Now write the total money equation

    15x + 7*(21-x) = 243  dollars.


Simplify and find x

    15x + 147 - 7x = 243

    15x - 7x = 243 - 147

        8x   =    96

         x   =    96/8 = 12.


ANSWER.  12 helmets.

Solved.



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