A larger number is five more than twice a smaller number. Their sum is 80. Find the numbers.

The smaller number is 25 and the larger number is 55.

Step-by-step explanation:

1. Let's call the larger number a and the smaller number b.

2. If the larger number is five more ( + 5) than twice (*2) the smaller number, we can write this as:

a = 2b + 5

3. Given that the sum of the larger and smaller number is 80, we can also write the following equation:

a + b = 80

4. We now have two equations:

(1) a = 2b + 5

(2) a + b = 80

Our aim is to now find the values of a and b. There are many different ways to continue from here, however since the first equation is already in terms of a, I would personally substitute this into the second equation:

given that a = 2b + 5:

a + b = 80

2b + 5 + b = 80 (Substitute a for 2b + 5)

3b + 5 = 80 (Add 2b and b)

3b = 75 (Subtract 5 from both sides)

b = 25 (Divide both sides by 3)

5. Now, given that b = 25, we can substitute this into equation (1) to get:

a = 2b + 5

a = 2 (25) + 5

a = 50 + 5

a = 55

6. Thus, the smaller number is 25 and the larger number is 55.

The first number is 25. The larger number is 55

Step-by-step explanation:

There was a lot of trial and error but it works. 25*2=50

50+5=55

55+25=80