Question

The sum of two numbers is 90. the larger number is 6 less than twice the smaller. find the numbers.

Answer 1

Answer:

32 and 58

Step-by-step explanation:

Let's set up equations.

The sum of two numbers (x and y) is 90: x + y = 90

The larger number (y) is 6 less than twice the smaller number (x): y = 2x - 6

We have our system of equations:

x + y = 90

y = 2x - 6

Let's use substitution.

Substitute y = 2x - 6 into the first equation.

x + y = 90

x + (2x - 6) = 90

Combine like terms.

x + 2x - 6 = 90

3x - 6 = 90

Add 6 to both sides to isolate x.

3x = 96

Divide both sides by 3 to further isolate x.

x = 32

Now that we know x, let's find y.

Plug in x = 32 into one of our original equations.

y = 2x - 6

y = 2(32) - 6

Multiply.

y = 64 - 6

y = 58

Now we have x = 32, y = 58.

Check your answer by plugging these values into one of our original equations.

x + y = 90

32 + 58 = 90

Add.

90 = 90

Your solution is correct.

Hope this helps!