This problem can be solved with a system of equations.
The variables we will use to solve this will be x, y, and z.
x will represent the first number.
y will represent the second number.
z will represent the third number.
The first equation in the system of equations we need to solve this is that the sum of all 3 numbers, x, y, and z, is 79.
x + y + z = 79
We are told the second number is 5 times greater than the first number.
Since y is the second number and x is the first number, this means y = 5x.
The last equation we'll be using to solve for the numbers is z = x + 16. This is because the third number, z, is 16 more, meaning plus, the first number, x.
{ x + y + z = 79
{ y = 5x
{ z = x + 16
Since y and z are already isolated, we can plug in the expressions equal to them in the first equation, x + y + z = 79.
x + (5x) + (x + 16) = 79
If we combine like terms then isolate the variable, we can solve for x. Then we can plug the value of x into the other two equations to solve for y and z.
Combining like terms:
x + (5x) + (x + 16) = 79
The like terms are x, 5x, and x.
x + 5x + x = 7x
7x + 16 = 79
Isolating the variable:
7x + 16 = 79
First, subtract 16 from both sides. Then, divide both sides by 7.
7x + 16 - 16 = 7x
79 - 16 = 63
7x / 7 = x
63 / 7 = 9
x = 9
Now that we know the value of x, we can plug it into the other two equations and solve for y and z.
Recall that y = 5x and z = x + 16.
Solving for y:
y = 5x
x = 9
y = 5(9)
5 • 9 = 45
y = 45
Solving for z:
z = x + 16
x = 9
z = 9 + 16
9 + 16 = 25
z = 25
Answers:
x = 9
y = 45
z = 25
Hope this helps!
