Question

1) A company sells boxes of cow bells (b) for $20 and boxes of air horns (h) for $30.

They can make a batch of cow bells that fills 8 boxes or a batch of air horns that fills 9 boxes.
The company only has 53 boxes. Which system of equations helps the company plan to make $275?

A. b = 53 - h
8b + 9h = 53


B. 8b = 53 - 9h
20b + 30h = 275

C. b = 53 - h
20b + 30h = 275

D. 8b = 53 - 9h
20b - 30h = 275

2) Captain Stacey is going to load her sailboat with jars of honey. She has room for 11 jars. She has allotted for 58 pounds of honey on her boat. She can choose from 3-pound jars (the variable j) or 7-pound jars (the variable h). Which equations would be a constraint to Captain Stacey maximizing her honey load?

a. j - h = 11

b.j = 11 + h

c.3j = 58 + 7h

d.3j = 58 - 7h

Answer 1

1.) The answer for this one is B. 8b = 53 - 9h and 20b + 30h = 275.
The first condition stated that the company only has 53 boxes available which can only have 8 boxes of cowbells and 9 boxes of air horns. The equation is 8b+9h = 53. By subtracting the two sides of the equation with 9h it will be equal to 8b= 53-9h. The second condition is that the price of the cow bells (b) is $20 and the price of the air horns (h) 30$ and a plan to make $275 is described by the equation: 20b + 30h =275.

2.) The first constraint is j+h=11 which is not in the choices. This is the equation in relation to the number of jars Captain Stacey should only have. The second constraint is in relation to the pounds honey she should have. To maximize her honey load, the equation should be: 3j + 7h= 58 which is equal to 3j = 58- 7h via the subtraction property of equations. The answer is letter D.