Question

A woman buys 50 eggs for $6.60. Some cost 12 cents each and 14 cents each. How many of each kind of eggs has she bought?

Answer 1

Answer:

......Hope it helps! Buddy.....

Answer 2

Given,

A woman buys 50 eggs for $6.60. Some cost 12 cents each and 14 cents each.

To Find,

How many of each kind of eggs has she bought?

Solution,

We can solve the question as follows:
It is given that a woman buys 50 eggs for $6.60. Some cost 12 cents each and 14 cents each. We have to find the number of each kind of eggs she bought.

Let the total number of the first kind of eggs she bought be x and the second kind be y.

$Number\: of\: eggs\: of\: the first\: kind = x$

$Number\: of\: eggs\: of\: the second\: kind = y$

The cost of the first kind is 12 cents each and the cost of the second kind is 14 cents each. The total cost is $6.60.

Since the cost is in dollars, we will convert it to cents.

$1$ $ $= 100\: cents$

$6.60$ $ $= 600 + 60 = 600\: cents$

Therefore,

$12x + 14y = 660$  ----------- (2)

Also, the total number of eggs she bought is 50. Therefore,

$x + y = 50$             ----------- (1)

Now, we will solve equations (1) and (2) to find each kind of eggs.

From equation (1),

$x = 50 - y$

Substituting x = 50 - y in equation (2),

$12(50 - y) + 14y = 660$

$600 - 12y + 14y = 660$

$600 + 2y = 660$

$2y = 660 - 600$

$2y = 60$

$y = \frac{60}{2} = 30$

Substituting y = 30 in x = 50 - y,

$x = 50 - 30 = 20$

Hence, she bought 20 eggs of the first kind and 30 eggs of the second kind.