Question

Four times a number plus 6 times another number is 20. The sum of the two numbers is 6.

What are the numbers?
2. Both numbers are 2
h 2 ands
8 and -2
d It is not possible to determine the numbers with the given information
Who can find the answers

Answer 1

Multi-step Word Equations

To translate word equations into numbers, we can change certain keywords into operations or numbers.

• four times/two times/three times etc. = multiply by 4/2/3 etc.
• 'a number'/'another number'/'the number' = variables
• sum = add
• times = multiply
• is = equals

Solving the Question

Let the two numbers be a and b.

We're given:

• 4 times a plus 6 times b is 20
  ⇒
  `4a+6b=20`
• The sum of a and b is 6
  ⇒
  `a+b=6`

First, isolate a in the second equation and substitute it into the first equation to solve for b:

`a+b=6\\a=6-b`

`4a+6b=20\\4(6-b)+6b=20\\24-4b+6b=20\\24+2b=20\\2b=-4\\b=-2`

Therefore, one of the numbers is -2. Plug this into the second equation to solve for the another number:

`a+b=6\\a-2=6\\a=8`

Therefore, the second number is 8.

Answer

The two numbers are 8 and -2.