18 and 35. The numbers whose sum 53 are 18 and 35.
The key to solve this problem is using a system of equations.
There are two numbers whose sum is 53. This number can be represented as x and y. So:
x + y = 53
Three times the smaller number is equal to 19 more than the larger. Let's set x as the smaller number and y the larger number. So:
3x = 19 + y
Clear y in both equations and let's use the equalization method to solve for x:
y = 53 - x and y = 3x - 19
Then,
53 - x = 3x - 19
53 + 19 = 3x + x ---------> 3x + x = 53 + 19 -------> 4x = 72
x = 72/4 = 18
To find y, let's substitute x = 18 in the equation x + y = 53
18 + y = 53 --------> y = 53 - 18
y = 35
<h3>Given</h3>
... r + 7 = 9
<h3>Find</h3>
... r
<h3>Solution</h3>
Subtract 7 from both sides of the equation.
... r + 7 - 7 = 9 - 7
... r = 2 . . . . . . simplify
Expressed as a solution set, this may look like ...
... r ∈ {2}
_____
You probably had no trouble solving this in 2nd grade when it was shown to you in the form ...
__ + 7 = 9
The answer which we found by inspection is
B. f(x) = -1/2x + 3
