I have 4 questions i’m confused about and I need help

Question

1. One number is 11 more than 3 times another number. Their sum is 71. Find the smaller number.

2. Two angles are complementary. One angle measures 22 degrees more than the other angle. Find the measure of the larger angle.

3. Two angles are supplementary. One angle measures 40 degrees more than the other angle. Find the measure of the larger angle.

4. The sum of three consecutive even integers is -36. Determine the largest integer of the three.

Answer 1

All of these questions are centered around the same root of mathematics, understanding definitions as well as learning how to interpret words and translating them into an equation.

1. From the first question we have two numbers x+y that total 71, or x+y=71. However, it gives much more information about one of the numbers. It states that one of the numbers is 11 more than 3 times the smaller number. Then, we can translate our first equation into x+(3x+11)=71. If we solve for x we will find the smaller number:

4x+11=71 => 4x=60 => x=15

1. The second question boils down to a similar thinking process as well as the definition of complementary (or summing to 90 degrees). We have:

2x+22=90 => 2x=68 => x=34

This is the measure of the smaller angle as I have set the equation up to solve for it. Then, the larger angle is 34+22=56. Alternatively, you could set up the equation as 2x-22=90 to solve for the larger angle from the beginning.

1. Similar to the prior, but we must know that supplementary angles sum to 180. We have:

2x-40=180 => 2x=220 => x=110

This is the measure of the larger angle, and you can check using the definition of supplementary. If the larger angle is 110, then the smaller angle is 40 less which is 70. So we have that 110+70=180 which fits our criteria for our solution.

1. The last one is a little more tricky, but it is the same concept of translating words into equations. They key is they are even integers, which means that each would be exactly two apart either -2 or +2 depending on what you would like to solve for. Since, we want to solve for the largest integer, and we know the sum is negative, we would ideally go with +2 when setting up since we want to find the largest negative number in this case. We have:

x+(x+2)+(x+4)=-36 => 3x+6=-36 => 3x=-30 => x=-10.

Answer 2

1) n + (3n + 11) = 71

2) a + 72 = 90

3) a + 40 = 180

4) n + (n + 1) + (n + 2) = -36