To solve the problem, we start by substituting the values of a and b into the expressions. Given that a = 111 and b = 111, let’s first calculate the two expressions separately.
Step 1: Calculate 5a + 4b + 15
- 5a = 5 * 111 = 555
- 4b = 4 * 111 = 444
- Therefore, 5a + 4b + 15 = 555 + 444 + 15 = 1114
Step 2: Calculate 5a + 4b + 3
- Using the values we calculated for 5a and 4b, we have 5a + 4b + 3 = 555 + 444 + 3 = 1002
Step 3: Calculate the ratio
The ratio of the two expressions is:
Ratio = (5a + 4b + 15) : (5a + 4b + 3) = 1114 : 1002
Step 4: Simplifying the ratio
To simplify the ratio, we can divide both numbers by their greatest common divisor. The GCD of 1114 and 1002 is 2. Therefore:
- 1114 ÷ 2 = 557
- 1002 ÷ 2 = 501
The simplified ratio is:
Ratio = 557 : 501