What is the value of xx in the equation 1/5x -2/3 y=30,15x−23y=30, when y=15y=15?

1 Answer
George P.
Jun 25, 2016

x = 200x=200

Explanation:

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

(1/5)x - (2/3)(15) = 30(15)x−(23)(15)=30
Now at this stage we could use a calculator to figure out what 2/323 of 1515 are though a bit of mental math is as easy:

(15/3) * 2 = 5 * 2 = 10(153)⋅2=5⋅2=10 (the dots mean multiply)

okay so now we have:

(1/5)x - 10 = 30(15)x−10=30 add 10 to both sides to get rid of the -10−10

(1/5)x = 40(15)x=40 let's get rid of that fraction by multiplying by 55

x = 200x=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(15)(200)−(23)(15)=30

now 200 / 5 = 402005=40 and we already know what 2/323 of 1515 is so :
that means

40 - 10 = 3040−10=30 which is ✓

Therefore we know our solution is right.

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