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The manager of a small supermarket placed an order for potatoes, onions and carrots totaling $880. For every 9 pounds of potatoes he ordered 4 pounds of onions and for every 5 pounds of onions he ordered 3 pounds of carrots. The total weight of the order was 770 pounds. If it is know that the cost of the onions is $1.25 per pound and the per pound cost of carrots is 50 cents more than that of potatoes, find the total cost of 5 pounds of potatoes, 2 pounds of onions and a pound of carrots.

Respuesta :

Answer: $9


Step-by-step explanation:

Step 1: calculation of weight of the potatoes, onions and carrots.

According to the question,

Ratio of weight of potatoes and onions= 9:5

And the ratio of weight of onions and carrots= 5:3

So,

The ratio of weight of potatoes, onions and carrots= 45:20:12

The weight of potatoes, onions and carrots= 45x, 20x, and 12x

Total weight of the order= 770

45x + 20x + 12x = 770

77x =770

x= 10

Therefore, the weight of potatoes, onions and carrots are 450 pounds, 200 pounds, and 120 pounds respectively.


Step 2: Calculation of cost per pound of potatoes and carrots.

Suppose, cost per pound of potatoes = y

So, cost per pound of carrots= y + 0.50

Now,

Total cost of order= $880

450y + 1.25*200 + (y + 0.50)*120 = 880

450y + 250 + 120y + 60 = 880

570y = 880 – 310

570y = 570

y = 1

Therefore, the cost per pound of potatoes= $1

And the cost per pound of carrots= $1.50


Step 3: To find the total cost of 5 pounds of potatoes, 2 pounds of onions and a pound of carrots.

Total cost= 5*1 + 2*1.25 + 1*1.50

Total cost= $9




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