Question

A grocer has two kinds of candy, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?

Answer 1

Answer:

Therefore, the grocer must use 55 pounds of the 40-cent candy and 45 pounds of the $1.40 candy to make 100 pounds worth 85 cents a pound

Step by step explanation:

Let x be the number of pounds of the 40-cent candy and y be the number of pounds of the $1.40 candy.

We can set up a system of equations based on the information given:

x + y = 100 (1) (the total amount is 100 pounds)
0.4x + 1.4y = 0.85(100) (2) (the cost of 100 pounds is $85)

Simplifying equation (2), we get:

0.4x + 1.4y = 85

Multiplying both sides by 10, we get:

4x + 14y = 850 (3)

Now, we can use equations (1) and (3) to solve for x and y. We can solve equation (1) for x:

x = 100 - y

Substituting this expression for x into equation (3), we get:

4(100 - y) + 14y = 850

Expanding and simplifying, we get:

400 - 4y + 14y = 850

10y = 450

y = 45

Substituting y = 45 into equation (1), we get:

x + 45 = 100

x = 55

Therefore, the grocer must use 55 pounds of the 40-cent candy and 45 pounds of the $1.40 candy to make 100 pounds worth 85 cents a pound.

Answer 2

Answer:The quantity of grocer of price $1.40 is 45 pounds

The quantity of grocer of price 40 cents is 55 pounds

Explanation:

Let The quantity of one grocer = x pound

Let The quantity of other grocer = y pound

The selling price of x grocer = 40 cents per pound

The selling price of y grocer = $ 1.40 per pound = 1.40 × 100 = 140 cents

Total quantity = 100 pounds

Total price of both grocer = 85 cents

According to question

x + y = 100 .........A

And

40 × x + 140 y = 85 × 100

Or, 40 x + 140 y = 8500 ........B

Solving eq A and eq b

(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100

Or, (40 x - 40 x) + (140 y - 40 y) = 8500 - 4000

or, 0 + 100 y = 4500

∴ y =

i.e y = 45 pounds

So, The quantity of grocer of price $1.40 = y = 45 pounds

Again

Put the vaue of y in eq A

x + y = 100

i.e x = 100 - y

or, x = 100 - 45

∴ x = 55 pounds

So, The quantity of grocer of price 40 cents = x = 55 pounds

Hence, The quantity of grocer of price $1.40 is 45 pounds

And The quantity of grocer of price 40 cents is 55 pounds Answer