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?

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

expression #3 is not equivalent. the others are.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.