Question

Martina, Bill, and Shen served a total of 70 orders Monday at the school cafeteria. Martina served 5 fewer orders than Shen. Bill served 3 times as many orders as Shen. How many orders did they each serve?

Answer 1

Shen = 15 Bill = 45 Martha = 10

Explanation:

M= Martha's orders

B= Bill's orders

S= Shen's orders

M+B+S = 70 (All together they have 70 orders)

S-5 = M (Martha = Shen - 5)

3S = B (3 times Bills orders = Shen)

First, plug in the third equation into the first.

M+3S+S= 70 ( notice how because 3S is equal to B we can plug the 3S in in place of the B)

Next, plug in the second equation into the new equation that we just made in order to replace the M.

S-5+3S+S= 70

Now combine like terms to get

5S-5 = 70

Add five on both sides to get

5S = 75

get the S alone by dividing both sides by 5 to get

S = 15

Now you are able to plug in your answer into the original three equations to find the other two answers so

S = 15 S = 15

3S = B S-5 = M

3(15) = B 15-5 = M

45 = B 10 = M

And just to double-check that you got the correct answers, plug your answers into the original first equation

B= 45 M=10 S=15

M+B+S = 70

Does your M + B + S = 70?

45+15+10 does in fact = 70 so our answers are correct

Answer 2

Shen's = 15

Martina's = 10

Bill's = 45

Explanation:

Let Shen's order served = S

Martina's = S - 5

Bill's = 3S

S + S - 5 + 3S = 70

5S = 70 + 5

5S = 75

S = 15

∴ Shen's = 15

Martina's = S - 5 → 15 - 5 = 10

Bill's = 3S → 3(15) = 45

15 + 10 + 45 = 70