jane, bob, and tony served a total of 50 orders monday at the school cafeteria. bob served 2 times as many orders as tony. jane’s served 10 fewer orders than tony. how many did each serve?

Answer 1

There are two critical items should you should do EVERY time you solve a word problem. The first is to define your variables.

Let j = the number of cafeteria orders that Jane served.

Let b = the number of cafeteria orders that Bob served.

Let t = the number of cafeteria orders that Tony served.

Next translate the words into mathematical equations (or inequalities if that is the case):

j + b + c = 50 (total orders served)

Since Bob served twice as many orders as Tony,

b = 2 * t

And we are told that Jane served 10 fewer orders than Tony, so

j = t - 10

The two most common ways of solving a 3 by 3 system of linear equation are substutution and elimination.

(These are linear equations because no two variables are either multiplied together, divided together, nor does any variable have an exponent other than 1.)

Substitution works best here because we have equations that eliminates two variables and converts the system into 1 equation in 1 unkown:

( t - 10 ) + ( 2 * t ) + t = 50

Simplifying,

t -10 + 2t + t = 50

Next, gather like terms on opposite sides of the equals sign:

4t = 60

Dividing by the coefficient of the variable:

t = 15

Now, the most important step that you should NEVER forget: CHECK YOUR ANSWER!

j = t - 10 = 15 - 10 = 5

b = 2 * t = 2 * 15 = 30

AND finally, 5 + 30 + 15 = 50, which verifies all of the given equations.

The right answer to the wrong problem usually gets you no points!

Answer 2

J = number of Jane served, B = number of Bob served, T = number of Tony served

J + B +T = 50 . . . . .. . .# 1

B = 2T . . . . . . # 2

J = T - 10 . . . . . . # 3

#2,3 we substitute into #1 equation, then

(T - 10) + 2T + T = 50

4 T - 10 = 50

4 T = 60

T = 15

B = 2 T = 30

J = T - 10 = 5