You buy #x# bottles of face paint and #y# brushes at two stores. The amounts you spend are represented by #10x +7.5y = 42.5# and #8x + 6y =34#. How many bottles of face paint and brushes did you buy?

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Answer 1 · 2017-12-07T06:52:08

Just arrange equations

#10x + 7.5y = 42.5#
#8x -6y = 34#

just multiply the second equation by #-10/8#

#10x + 7.5y = 42.5#
#-10x + (60y)/8 = -340/8#

Add these two equations:

#7.5 y + (15y)/2 = 42.5 - 42.5#

#(15y + 15y)/2 = 0#

Therefore you cannot buy brushes. x will be

#10x = 42.5#

#x=4.25# (face paint). It also satisfies the second original equation. But I am not sure whether I can buy a quarter bottle (unit) of face paint.