Question 1193922
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A setup for solving the problem using formal algebra....<br>
x+y=21  (the total number of items was 21)
15x+7y=243  (the total cost was $243)<br>
With the two equations in that form, I would solve using elimination:<br>
7x+7y=147  (first equation, multiplied by 7)
15x+7y=243
8x=96  (difference between the two equations)<br>
I'll let you finish; it's basic algebra.<br>
An informal solution, using logical reasoning and mental arithmetic (which gives you better mental exercise than using formal algebra....):<br>
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.<br>
Try each possibility to see which one satisfies all the conditions of the problem.<br>