Question

The sum of two numbers is 5, and the difference between the first number and twice the second number is 29.

Answer 1

Converting Words into Equations

We can convert word problems into equations by translating key terms into operations:

• sum = we add
• difference = we subtract
• twice = multiply by 2
• is = equals

Solving the Question

We're given:

• sum of two numbers is 5
• difference between the first number and twice the second number is 29

Let the first number be a and the second number be b.

Translate the words into numbers:

• sum of two numbers is 5
  
  `a+b=5`
• difference between the first number and twice the second number is 29
  
  `a-2b=29`

Subtract the second equation from the first to isolate b:

`(a+b)-(a-2b)\\=a+b-a+2b\\=b+2b\\=3b`

`5-29\\=-24`

`3b=-24\\b=-8`

Therefore b is -8.

Substitute b back into the first equation to find a:

`a+b=5\\a-8=5\\a=13`

Therefore, a is 13.

Answer

a = 13

b = -8