What is the value of #x# in the equation #1/5x -2/3 y=30,# when #y=15#?

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Answer 1 · 2016-06-25T17:40:51

#x = 200#

Okay so we can start by substituting in #y# as we know what it is already:

#(1/5)x - (2/3)(15) = 30#
Now at this stage we could use a calculator to figure out what #2/3# of #15# are though a bit of mental math is as easy:

#(15/3) * 2 = 5 * 2 = 10# (the dots mean multiply)

okay so now we have:

#(1/5)x - 10 = 30# add 10 to both sides to get rid of the #-10#

#(1/5)x = 40# let's get rid of that fraction by multiplying by #5#

#x = 200# and there's the solution for x

We can check we got this right by substituting it back into the original equation with the known y:

#(1/5)(200)-(2/3)(15) = 30#

now #200 / 5 = 40# and we already know what #2/3# of #15# is so :
that means

#40 - 10 = 30# which is ✓

Therefore we know our solution is right.