Question

Let x, y, z, and w represent the population in millions of four cities A, B, C, and D, respectively. Express the given statement as an equation in x, y, z, and w. If the equation is linear, express it in the standard form

ax + by + cz + dw = k.
(If the equation is not linear, enter NONLINEAR.)
City A has three times as many people as cities B and C combined

Answer 1

x -3y -3z = 0

Explanation:

You want to write "City A has three times as many people as cities B and C combined" as an equation in standard form, letting x, y, z, w represent the populations of cities A, B, C, D, respectively.

Translation

The populations of cites B and C combined can be expressed by ...

y +z

Three times the combined population is then ...

3(y +z)

This is equal to the population of city A, so we can write ...

x = 3(y +z)

Standard form

This equation is in standard form when all of the variable terms are on one side of the equal sign, and the expression is simplified.

x -3(y +z) = 0 . . . . . . . subtract the right side expression

x -3y -3z = 0 . . . . . . . eliminate parentheses; standard form