Question

Mr. Hammond is the volunteer coordinator for a company that puts on running races. Last year, the company organized 7 short races and 8 long races, which required a total of 804 volunteers. This year, the company organized 11 short races and 5 long races, which required 688 volunteers in total. How many volunteers does each type of race require?

Answer 1

Answer:

28 short race volunteers

76 long race volunteers

Step-by-step explanation:

Let :

Short races = a

Long races = b

LAST YEAR:

7a + 8b = 804 - - - - (1)

THIS YEAR:

11a + 5b = 688 - - - (2)

Multiply (1) by 5 and (2) by 8

35a + 40b = 4020

88a + 40b = 5504

Subtract

-53a = - 1484

a = 1484 / 53

a = 28

Put a = 28 in equation (1)

7(28) + 8b = 804

196 + 8b = 804

8b = 804 - 196

8b = 608

b = 76

28 short race volunteers

76 long race volunteers