SOLUTION: When 3 times the sum of 4 and an unknown number is subtracted from 10 times the unknown number, the result is equal to 5 times the sum of 9 and twice the unknown number. Find the n

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Question 202164: When 3 times the sum of 4 and an unknown number is subtracted from 10 times the unknown number, the result is equal to 5 times the sum of 9 and twice the unknown number. Find the number.
Found 2 solutions by RAY100, PRMath:
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
10x -[ 3* (4+x) } = 5*(9+2x)
10x -12 -3x = 45 +10x
-3x = 57
x=-19
.
check
10(-19) - {3*(4-19)} =5{9+2(-19)}
-190 +45 = -145
-145 = -145,,,,,,ok

Answer by PRMath(133) (Show Source):
You can put this solution on YOUR website!
When 3 times the sum of 4 and an unknown number is subtracted from 10 times the unknown number, the result is equal to 5 times the sum of 9 and twice the unknown number. Find the number.

You just have to translate these phrases into equations.

Just take a little at a time. We'll break the sentence down into phrases:

Phrase 1: When 3 times the sum of 4 and an unknown number
Equation: 3(4 + x) (We made the unknown number "x")

Phrase 2: (The above equation) is subtracted from 10 times the unknown number
Equation: 10x - 3(4 + x)

Phrase 3: the result is equal
Equation: =

Phrase 4: to 5 times the sum of 9 and twice the unknown number
Equation: 5(9 + 2x)

Put it all together:

10x - 3(4 + x) = 5(9 + 2x) Now solve for x
10x - 12 - 3x = 45 + 10x (Distributed the "3" and the "5"
7x - 12 = 45 + 10x (combined like terms)
-3x - 12 = 45 (subtracted 10x from both sides)
-3x = 57 (added 12 to both sides)
x = -19