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:

short races require 28 volunteers while long races require 76 volunteers

Step-by-step explanation:

First, lets turn the sentences into a math problem we can solve.

short races= s

long races= l

"The company organized 7 short races and 8 long races, which required a total of 804 volunteers"

7s+8l=804

"This year, the company organized 11 short races and 5 long races, which required 688 volunteers in total."

11s+5l=688

First, lets find out the value of short races in terms of long races. To do this, lets use the first equation and solve for s.

7s+8l=804 (Subtract 8l from both sides)

7s=-8l+804 (Divide both sides by 7 to just get x)

s=-8/7l + 804/7

Now that we "know" the value of s, lets plug it into the second equation.

11s+5l=688 (Substitute in our value of s)

11 (-8/7l + 804/7)+5l=688 (Simplify)

-88/7l + 8844/7 + 5l = 688 (Add 8844/7 to both sides)

-88/7l + 5l = -4028 (Combine both ls)

-53/7l = -4028 (Multiply both sides by -7/53 to get l)

l=76

Now that we know the value of l, lets plug it into our first equation

7s+8l=804 (Substitute in the value of l)

7s+8(76)=804 (Multiply)

7s+608=804 (Subtract 608 from both sides)

7s=196 (Divide by 7 to get the value of s)

s=28

So, s=28 and l=76

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