. Three times one number is equal to two times the larger one and their difference is 1. What are the numbers?

Answer 1

This problem can be solve using a system of equations.

3x = 2y

y - x = 1 (letting y be the bigger number)

Use the substitution method to solve the system. Solving for y in the second equation is quite simple.

y = x + 1

Replace y in the first equation with x + 1.

3x = 2(x + 1)

Then, solve for x.

3x = 2x + 2

x = 2

Use the value of x to find y.

y - 2 = 1

y = 3

The numbers and 2 and 3. Notice that they satisfy both equations.

3x = 2y

3(2) = 2(3)

y - x = 1

3 - 2 = 1

:)

Answer 2

Hi Sue F

Is it correct to assume that one number is smaller than the other number? you just called one number but information implies that one number must be smaller than the other.

Smaller number is 2

Larger number is 3

Let smaller number = x

Let larger number = y

We are given

3x = 2y

We are also given that the difference between one number and the larger number is 1

y - x = 1

y = x + 1

By substitution we have

3x = 2(x + 1)

3x = 2x + 2

3x - 2x = 2

x = 2

3(2) = 6

6 = 2y

6/2 = y

3 = y

This can also be done with elimination since

3x = 2y

Then 3x - 2y = 0 could be equation 1

And y - x = 1 could be equation 2

We have

3x - 2y = 0

-x + y = 1

If you multiply equation 2 by 3

3(-x + y = 1) then we have

-3x + 3y = 3

3x - 2y = 0

Combining these two equations we eliminate x to give

y = 3

Checking

3x = 2y

3(2) = 2(3)

and

y - x = 1

3 - 2 = 1

I hope this helps.

Answer 3

X = an unknown number

Y = a larger unknown number

3 times an unknown number is equal to 2 times the larger number

3x = 2y

x - y = 1

x - y = 1

- x. - x

y = 1 - x

Substitute "1 - x" for y in the first equation

3x = 2(1 - x)

3x = 2 - 2x

+2x. +2x

5x = 2

÷5. ÷5

x = 2/5

Now, if x - y =1 & x = 2/5, then

2/5 - y = 1

-2/5. -2/5

-y = 3/5

÷-1. ÷-1

y = -3/5