Answer:
x + y = 90
x = 14 + 3y
The numbers are 71 and 19.
Step-by-step explanation:
Let the larger number be x.
Let the smaller number be y.
The sum of the numbers is 90.
x + y = 90
The larger number, x, is 14 more than 3 times the smaller number, y.
x = 14 + 3y
We have a system of two equations in two unknowns.
x + y = 90
x = 14 + 3y
Since the second equation is already solved for x, we will use the substitution method to solve the system of equations.
Substitute x in the first equation with 14 + 3y.
x + y = 90; x = 14 + 3y
14 + 3y + y = 90
Combine like terms on the left side.
4y + 14 = 90
Subtract 14 from both sides.
4y = 76
Divide both sides by 4.
y = 19
The smaller number is 19.
Now we substitute 19 for y in the first equation and solve for x.
x + y = 90; y = 19
x + 19 = 90
Subtract 19 from both sides.
x = 71
The larger number is 71.
Answer: The numbers are 71 and 19.
