Question

Seven-tenths of a number decreased by thirteen is equal to three-tenths the number increased by 13. Find the number.

Answer 1

Create an equation from the word problem. 'of' indicates multiplication, 'decreased' indicates subtraction, 'increased' indicates addition. Let's use 'x' for the number.


`\sf(7)/(10)x-13=(3)/(10)x+13`

Now solve for 'x'. Subtract 3/10x to both sides:


`\sf(4)/(10)x-13=13`

Add 13 to both sides:


`\sf(4)/(10)x=26`

Divide 4/10 to both sides or multiply by its reciprocal, 10/4:


`\sf x=\boxed{\sf 65}`