Question #27c32

1 Answer
MJ
Dec 19, 2017

Vests = 60

Explanation:

Let's assume that the following purchases were made:
Vests = #x#
Soccer balls = #y#
Cones = #y+40# (because 40 more cones were purchased than soccer balls)

The total purchased items = #164#

It can be written in equation form as:
#x+y +(y+40) = 164#
or, #x+y+y+40 = 164#
or, #x+2y+40 = 164#............(1)

Now the total cost of purchase was = #$500#
Therefore, all items purchased with their individual costs should equal #$500#

This can be represented in an equation as follows:
#2.5x+9.25y+ 0.75(y+40) = 500#
or, #2.5x + 9.25y + 0.75y + 30 = 500#, where (#0.75xx40 = 30)#
or, #2.5x+10y+30 = 500#.................(#2#)

Now, solving equation #(1)# and #(2)#

#x+2y+40 = 164#
#2.5x+10y+30 = 500#
To solve this equation, one of the unknown terms has to be cancelled or removed.
To make that happen, let's multiply #x+2y+40 = 164# by 2.5 and that will help remove the #x# factor from the equation by subtraction.

After multiplication by 2.5, #x+2y+40 = 164# becomes:
#2.5x+5y+100 = 410#............#(3)#

Now subtracting equation #(3)# from equation (#2#)

#cancel2.5x+10y+30 = 500#
#-(cancel2.5x+cancel5y^(5y)+cancel 100^-70 = cancel410^90)#

Therefore, the new equation becomes:
#5y-70 = 90#
or, #5y = 160# or, #y = cancel160^32/cancel5^1# = #32#

Thus, the number of soccer balls = #32#
Number of cones = #32+40# = #72#
and, vests = #164 -72-32# = #60#

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