7 + 2f = cg
21g + 21 = 6f - 15g
If c is constant, and the system of equations shown above has infinitely many solutions, what is the value of c?

A) 12

B) 15

C) 10

D) 14

A company produces two types of widgets, A and B. The cost to produce each type includes a fixed setup cost plus a variable cost per unit. In one batch, producing 100 units of A and 200 units of B costs $1500. In another batch, producing 200 units of A and 300 units of B costs $2200. Determine the fixed setup cost and the variable cost per unit for both types.

A) Fixed cost is $800, type A is $0 and type B is $0.

B) Fixed cost is $800, type A is $7 and type B is $0.

C) Fixed cost is $800, type A is $0 and type B is $7.

D) Fixed cost is $800, type A is $7 and type B is $7.

Jane and John are selling cookies and brownies for a school fundraiser. They sold a total of 50 items on Monday, and 70 items on Tuesday. On Monday, Jane sold twice as many cookies as John, and on Tuesday, Jane sold three times as many cookies as John. How many cookies and brownies did each sell on each day?

A) John sold 20 cookies and 20 brownies on Monday.
Jane sold 40 cookies and 30 brownies on Tuesday.

B) John sold 20 cookies and 30 brownies on Monday.
Jane sold 40 cookies and 40 brownies on Tuesday.

C) John sold 20 cookies and 30 brownies on Monday.
Jane sold 40 cookies and 30 brownies on Tuesday.

D) None of the above

gx - hy = 78
4x + 3y = 13
In the system of equations above, g and h are constants. If the system has infinitely many solutions, what is the value of gh?

A) -423

B) 432

C) 423

D) -432

Determine whether the system of linear equations has an Infinite solution:
2x + y + z = 5, 3x + 5y + 2z = 15, 2x + y + 4z = 8

A) x = 2, y = 2 and z = 1

B) x = 1, y = 1 and z = 1

C) x = 1, y = 2 and z = 2

D) x = 1, y = 2 and z = 1

Sarah invests in two types of bonds. One bond pays 6% interest annually, and the other pays 8% interest annually. If she invests $5000 in each type of bond and receives $760 in interest in total, how much did she invest in each type of bond?

A) $3000 in the 6% bond and $7000 in the 8% bond

B) $4000 in the 6% bond and $6000 in the 8% bond

C) $2000 in the 6% bond and $8000 in the 8% bond

D) $6000 in the 6% bond and $10000 in the 8% bond

Given the system of equations: 3x + 5y = 15 and 9x + 15y = 45, show that the system has infinitely many solutions and determine one such solution.

A) x = 2 and y = 1

B) x = 0 and y = 3

C) x = 1 and y = 2

D) x = 3 and y = 0

A company mixes two types of nuts, one with a protein content of 10 grams per 100 grams and the other with 20 grams per 100 grams. They need to create a mixture with a protein content of 15 grams per 100 grams. What are the possible ratios of the two types of nuts they can use?

A) x : y = 100 : 75
and x : y = 100 : 25

B) x : y = 100 : 75
and x : y = 75 : 100

C) x : y = 25 : 100
and x : y = 100 : 25

D) x : y = 100 : 75
and x : y = 75 : 25

A chemist is mixing two solutions, one containing 40% acid and the other containing 60% acid. How much of each solution should be mixed to obtain a 50% acid solution if a total of 10 liters of the resulting mixture is needed?

A) 3 liters of the 40% acid solution and 7 liters of the 60% acid solution.

B) 5 liters of the 40% acid solution and 5 liters of the 60% acid solution.

C) 2 liters of the 40% acid solution and 8 liters of the 60% acid solution.

D) 4 liters of the 40% acid solution and 6 liters of the 60% acid solution.

- 15x + 25y = 65
One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which of the following could be the second equation in the system?

A) 12x + 20 y = 52

B) 12x + 20 y = -52

C) - 12x + 20 y = 52

D) - 12x + 20 y = - 52