Question

Twice The sum of a number and three times the second number is four. The difference of 10 times the second number And five times the first is 90 find the numbers

Answer 1

Answer: The first number is
`-10` and the second number is
`4`

Explanation:

Let be "x" the first number and "y" the second number.

The word "Twice" indicates multiplication.

By definition, the sum is the result of an addition.

"is" indicates an equal sign.

Therefore, "Twice the sum of a number and three times the second number is four" can be expressed as:

`2(x+3y)=4` [Equation 1]

A difference is the ressult of a subtraction, then " The difference of 10 times the second number and five times the first is 90" can be expressed as:

`10y-5x=90` [Equation 2]

To find the numbers:

1. Solve for "x" from the Equation 1:

`2(x+3y)=4\\\\2x+6y=4\\\\x=(4-6y)/(2)\\\\x=2-3y`

2. Substitute this equation into the Equation 2 and solve for "y":

`10y-5(2-3y)=90\\\\10y-10+15y=90\\\\25y=100\\\\y=(100)/(25)\\\\y=4`

3. Substitute the value of "y" into the equation
`x=2-3y` and evaluate:

`x=2-3(4)\\\\x=-10`