Ralph bought some magazines at $4 each and some dvds at $12 each. He spent $144 and bought a total of 20 items. How many magazines and how many movies did he buy?

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Answer 1 · 2018-03-20T04:20:15

Ralph bought #12# magazines and #8# dvds.

Let #m# be the number of magazines Ralph bought and #d# be the number of dvds he bought.

"Ralph bough some magazines at #$4# each and some dvds at #$12# each. He spent #$144#."

#(1)=>4m+12d=144#

"He bought a total of #20# items."

#(2)=>m+d=20#

We now have two equations and two unknowns, so we can solve the linear system.

From #(2)# we find:

#(3)=>m = 20-d#

Substituting #(3)# into #(1)#:

#4(20-d)+12d = 144#

#80-4d+12d = 144#

#8d+80=144#

#8d=64#

#=>color(blue)(d = 8)#

We can use this result in #(3)#:

#m = 20 - (8)#

#=>color(blue)(m = 12)#

Hence, Ralph bought #12# magazines and #8# dvds.