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
When the problem asks you to find the zeros all they are asking for is the solution so to solve all you need to do is set each individual piece equal to zero.
