Question

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?

Answer 1

Answer

Latoya served 14 orders.

Brian served 19 orders.

Hong served 57 orders.

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!!!