Question

One number is 2 more than 3 times another. Their sum is 22. Find the numbers.

Answer 1

To find the two numbers, create a system of equations and solve for the values of x and y. The two numbers are 17 and 5.

Step-by-step explanation:

To find the two numbers, let's create a system of equations based on the given information. Let one of the numbers be represented by x, and the other number be represented by y. From the problem, we know that one number is 2 more than 3 times the other, so we can write the equation: x = 3y + 2. Additionally, we know that the sum of the two numbers is 22, so we can write the equation: x + y = 22.

Using these two equations, we can solve for the values of x and y. Substituting the first equation into the second equation, we get: (3y + 2) + y = 22. Simplifying, we have: 4y + 2 = 22. Subtracting 2 from both sides, we get: 4y = 20. Dividing both sides by 4, we get: y = 5. Substituting this value back into the first equation, we get: x = 3(5) + 2, which simplifies to x = 17.

Therefore, the two numbers are 17 and 5.

Answer 2

Make a system of equations.


`\sf~x=3y+2`

`\sf~x+y=22`

Re-arrange the 2nd equation:


`\sf~x+y=22`

Subtract y to both sides:


`\sf~x=-y+22`

Plug in -y + 22 for 'x' in the first equation.


`\sf~x=3y+2`


`\sf~-y+22=3y+2`

Subtract 3y to both sides:


`\sf~-4y+22=2`

Subtract 22 to both sides:


`\sf~-4y=-20`

Divide -4 to both sides:


`\sf~y=\boxed{\sf5}`

Plug this into any of the two equations to find 'x':


`\sf~x+y=22`


`\sf~x+5=22`

Subtract 5 to both sides:


`\sf~x=\boxed{\sf17}`

So one of the numbers is 5 and one of them is 17.