Question

32 less than 3/7 of a number is 11/35 of that number. Find the number.

Answer 1

Answer is x=280
Step by step
We know 32 less than is subtraction -32
We know 3/7 of a number is 3/7x
We know “is” is equal =
We know 11/35 of a number is 11/35x
So
3/7x - 32= 11/35x

Now solve by first by combining like terms
Change the denominator of 3/7 to match the other fraction so we can combine. 7x5=35 so we do the same to the numerator, 3x5.
3. 15
____. _____
7. 35

3/7x -32 = 11/35x
15/35x - 32 = 11/35x
Subtract 15/35x from both sides to combine like terms
-32 = -4/35x
Now divide both sides by -4/35 to solve for x
To divide a fraction flip it and multiply
( -35/4 )(-32)
X= 280

You can check your work by substituting your number for x into your equation

3/7 (280) -32 = 11/35 (280)
120 - 32 = 88
88 = 88

Answer 2

Explanation:

Let "a number" be x.

"3/7 of a number" means (3/7)x

"32 less" means - 32

Thus, "32 less than 3/7 of a number" means (3/7)x -32

"is 11/35 of that number" means = (11/35)x

Put these together and we get:

(3/7)x -32 = (11/35)x

(3/7)x - (11/35)x = 32 Rearrang to get the x on one side

We need to change "(3/7)x - (11/35)" so that the two terms have a common denominator.

If we multiply the first term by (5/5) [which is equal to 1], we get:

(5/5)(3/7)x or

(15/35)x

We can now write:

(15/35)x - (11/35)x = 32

(4/35)x = 32

Multiply both sides by (35/4)

(35/4)(4/35)x = (35/4)(32)

x = (35)(8)

x = 280