The larger of two numbers is four more than the smaller number. If the sum of the numbers is 52. Find the numbers.

Smaller number = 24

Larger number = 28

Step-by-step explanation:

Given two different numbers that add up to 52, and have a larger number that it 4 greater than the smaller one, two equations can be formed:

x + y = 52

y = (x + 4)

Where x is the smaller number, and y is the larger one.

Then just substitute, and solve for x:

y = (x + 4) → x + y = 52

→

x + (x + 4) = 52

2x + 4 = 52

2x = 48

x = 24

Since we now know the smaller number, just substitute this back into the equation to find the larger one, remember the larger number is 4 greater than the smaller one.

24 [smaller number] + 4 [difference] = 28 [larger number].

24 [smaller number] + 28 [larger number] = 52 [sum of the numbers]

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation:

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal