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O LINEAR EQUATIONSSolving a word problem with three unknowns using a linear...Achley vAshley vEspanolLatoya, Brian, and Hong served a total of 90 orders Monday at the school cafeteria. Hong served 3 times as many orders asBrian. Latoya served 5 fewer orders than Brian. How many orders did they each serve?

User Jacob Tomlinson
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Answer

Latoya served 14 orders.

Brian served 19 orders.

Hong served 57 orders.

Step-by-step explanation

Let the number of orders served by Latoya, Brian and Hong on Monday at the school cafeteria be L. B and H respectively.

- Latoya, Brian, and Hong served a total of 90 orders Monday at the school cafeteria.

L + B + H = 90 ....... equation 1

- Hong served 3 times as many orders as Brian.

H = 3B ....... equation 2

- Latoya served 5 fewer orders than Brian.

L = B - 5 ...... equation 3

Writing the equations together

L + B + H = 90 ....... equation 1

H = 3B ....... equation 2

L = B - 5 ...... equation 3

Substituting for L and H in equation 1

L + B + H = 90

(B - 5) + B + 3B = 90

B - 5 + 4B = 90

5B - 5 = 90

5B = 90 + 5

5B = 95

Divide both sides by 5

(5B/5) = (95/5)

B = 19 orders

Recall,

H = 3B = 3 (19) = 57 orders.

L = B - 5 = 19 - 5 = 14 orders.

Hence,

Latoya served 14 orders.

Brian served 19 orders.

Hong served 57 orders.

Hope this Helps!!!

User Farahmand
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