Question

the sum of twice a number and a second number is 61. the second number is 17 less than four times the first. what are the two numbers?

Answer 1

We have two numbers, let's say a and b.

We must build our equations.

Sum = addition, and twice = multiplication, so:

$2a + b = 61$

where a represents "twice a number"

Less = subtraction, and four times = multiplication, so:

$b = 4a - 17$

Now we have our two equations:

$2a + b = 61\\b = 4a - 17$

One of these is already solved for a variable, so we can substitute it.

Substitute b into the first equation:

$2a + 4a - 17 = 61\\6a - 17 = 61\\6a = 78\\a = 13$

We have solved for a's int value, being 13.

Plug a into the second equation and solve for b:

$b = 4(13) - 17\\b = 52 - 17\\b = 35$

We have solved for b's integer value, 35.

Now that we have both numbers, let us check our solution:

a = 13

b = 35

The sum of twice a number and a second number is 61:

13(2) + 35 = 26 + 35 = 61 ✓

The second number is 17 less than four times the first:

35 = 4(13) - 17 = 52 - 17 = 35 ✓

Our answers are:

a = 13

b = 35