A cook used all of a two-pound chunk of cheese in making three recipes. Recipe I used one-third as much cheese as Recipe II did, and Recipe II used one-half as much cheese as Recipe III.

What part of the whole chunk of cheese, and how many pounds, did each recipe use?

Recipe I uses 10% of the whole chunk of cheese.

Recipe II uses 30% of the whole chunk of cheese.

Recipe II uses 60% of the whole chunk of cheese.

Recipe I uses 0.2 pounds of cheese.

Recipe II uses 0.6 pounds of cheese.

Recipe II uses 1.2 pounds of cheese.

Step-by-step explanation:

Total amount of cheese = 2 pounds

Recipe I used one-third as much cheese as Recipe II did, and Recipe II used one-half as much cheese as Recipe III.

Let the amount of cheese used by recipe I, II and III be x, y and z respectively.

Total amount of cheese = 2 pounds

x + y + z = 2 (eqn 1)

Recipe I used one-third as much cheese as Recipe II did

x = (1/3)y

y = 3x

Recipe II used one-half as much cheese as Recipe III.

y = (1/2)z

z = 2y

z = 2y = 2(3x) = 6x

Substituting all of these into eqn 1

x + y + z = 2

x + 3x + 6x = 2

10x = 2

x = 0.2 pounds of cheese

y = 3x = 0.6 pounds of cheese

z = 6x = 1.2 pounds of cheese.

Recipe I uses (0.2/2) = 10% of the whole chunk of cheese.

Recipe II uses (0.6/2) = 30% of the whole chunk of cheese.

Recipe II uses (1.2/2) = 60% of the whole chunk of cheese.

Hope this Helps!!!

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

slope is 35 and 20 miles is the y-intercept.

step-by-step explanation: