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
= 3