Answer:
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.
