Mary makes two sizes of mugs: a small mug that she sells for 2 dollars and 50 cents and a large mug that she sells for 5 dollars and 75 cents. Yesterday Mary made 56 dollars. Before she opened her shop in the morning, she had 200 mugs in her inventory. At the end of the day she has 188. How many large mugs did she sell? How many small mugs did she sell?

Question

Mary makes two sizes of mugs: a small mug that she sells for 2 dollars and 50 cents and a large mug that she sells for 5 dollars and 75 cents. Yesterday Mary made 56 dollars. Before she opened her shop in the morning, she had 200 mugs in her inventory. At the end of the day she has 188. How many large mugs did she sell? How many small mugs did she sell?

Answer 1

Let

x = # large mugs sold
y = # small mugs sold
so, what have they told you?
Total income: 2.50x + 5.75y = 56.00
mugs sold = 200-188 = 12. So, x+y = 12

Now just solve for x and y

Answer 2

200 - 188 = 12 Mugs sold.

Sold X small mugs.
Sold 12-X Large mugs.

2.5x + 5.75(12-x) = 56.
5x/2 + 23/4(12-x) = 56,
10x + 23(12-x) = 224,
1ox + 276 - 23x = 224,
X = ?
12-X = ?.

Answer 3

To find out how many large mugs Mary sold and how many small mugs she sold, we can use a system of equations. Let's assign variables to the unknowns:

Let's call the number of small mugs sold 's' and the number of large mugs sold 'l'.

We need to find the values of 's' and 'l' that satisfy the given conditions.

1) The total revenue Mary made from selling small mugs is given by 2.50 * s dollars.
2) The total revenue Mary made from selling large mugs is given by 5.75 * l dollars.
3) The total revenue Mary made yesterday is 56 dollars.

We can write the equations based on the information given:

Equation 1: 2.50s + 5.75l = 56 ----- (Equation for total revenue)

Now, let's consider the inventory:

4) Before Mary opened her shop in the morning, she had 200 mugs in her inventory.
5) At the end of the day, she had 188 mugs in her inventory.

The total number of mugs sold is equal to the difference between the starting and ending inventories.

Equation 2: s + l = 200 - 188 = 12 ----- (Equation for total number of mugs sold)

Now, we have a system of equations. We can solve this system using various methods, such as substitution or elimination. Let's solve it using substitution.

From Equation 2, we can express 'l' in terms of 's':

l = 12 - s

Now, substitute this value into Equation 1:

2.50s + 5.75(12 - s) = 56
2.50s + 69 - 5.75s = 56
-3.25s = 56 - 69
-3.25s = -13
s = -13 / -3.25
s = 4

So, Mary sold 4 small mugs.

Substitute this value of 's' back into Equation 2 to find 'l':

l = 12 - s
l = 12 - 4
l = 8

Therefore, Mary sold 8 large mugs.

To summarize:
Mary sold 4 small mugs and 8 large mugs.