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vodka [1.7K]
3 years ago
12

6. Bons grocer wishes to mix some nuts worth 90 cents per pound with some nuts worth $1.60 per pound to make 175 pounds of a mix

ture that is worth $1.30 per pound. How much of each should she use? Include your equation. *
Mathematics
2 answers:
Ivenika [448]3 years ago
7 0

Answer:

75 pounds and 100 pounds.

Step-by-step explanation:

Given:

Bons grocer wishes to mix some nuts worth 90 cents( $0.9) per pound with some nuts worth $1.60 per pound to make 175 pounds of a mixture that is worth $1.30 per pound.

Question asked:

How much of each should she use?

Solution:

Let there are two types of nuts mixed in the mixture, one is nut A and another is nut B.

As we know:

1 cent = $0.01

90 cents = $0.01 \times 90 = $0.9

Let quantity of nut A mixed = x\ pound

Quantity of nut B mixed = 175-x\ pound

Total quantity of mixture = 175 pounds

Total cost of mixture = Cost per pound \times Total quantity of mixture in pound

                                  = $1.30 \times 175 = $227.5

As mixture is prepared by mixing two types of nuts:-

Cost per pound of nut A \times Quantity mixed + Cost per pound of nut B

0.9x+1.60(175-x)=227.5\\0.9x+280-1.60x=227.5\\-0.7x+280=227.5\\

By subtracting both sides by 280

-0.7x=-52.5

Minus canceled by minus

0.7x=52.5\\Dividing\ both\ sides\ by\ 0.7\\x=75\ pound

Substituting the value:-

Quantity of nut A mixed = x\ pound = 75 pounds

Quantity of nut B mixed = 175-x\ pound= 175 - 75 = 100 pounds

Therefore, Bons grocer wishes to mix<u> 75 pounds of nuts worth 90 cents</u> ($0.9) with <u>100 pounds of some nuts worth $1.60 </u>per pound to make  175 pounds of a mixture that is worth $1.30 per pound.

Licemer1 [7]3 years ago
6 0

Answer:

The quantity of first mixture = x  = 75 pounds

The quantity of second mixture = 175 - x  = 175 - 75 = 100 pounds

Step-by-step explanation:

Total quantity of mixture = 175 pounds

Let quantity of first mixture = x

Quantity of second mixture = 175 - x

From the given information

x (0.9) + (175 - x) × 1.6 = 175 × 1.3

By solving above equation we get

0.9 x + 280 - 1.6 x = 227.5

0.7 x = 52.5

x = 75 pounds

Thus the quantity of first mixture = x  = 75 pounds

The quantity of second mixture = 175 - x  = 175 - 75 = 100 pounds

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