lizzie bought several apples at 20 cents each, ate two of them, and sold the rest for 30 cents each. she made a profit of $2.20. How many did she buy?

Mercedese had a total of 37 nickles, dimes, and quarters. She had 3 fewer dimes than nickels and 4 more quarters than nickels. How much money did she have?

She made a profit of a dime per apple. How many dimes are in $2.20? Then add two more for the apples she ate.

n = # nickels

d = # dimes
q = # quarters
==================
n+d+q=37
d = n-3
q=n+4
substitute d = n-3 and q = n+4 into the first equation, solve for n, then solve for d and q. I think n = 12 but check my thinking.
Post your work if you get stuck.

ok thanks-i understand both problems now!

To solve the first problem, we need to set up equations based on the given information.

Let's assume that Lizzie bought x apples.

The cost of each apple is 20 cents, so the cost of x apples would be 20x cents.

Lizzie ate two apples, so she sold the remaining (x - 2) apples for 30 cents each.

The revenue from selling the apples would be (x - 2) * 30 cents.

The profit is calculated by subtracting the cost from the revenue, and in this case, it is $2.20.

We can set up the equation as follows:

Revenue - Cost = Profit
(x - 2) * 30 - 20x = 220

Now, let's solve the equation:

30x - 60 - 20x = 220
10x = 280
x = 28

Therefore, Lizzie bought 28 apples.

To solve the second problem, we need to set up equations based on the given information.

Let's assume that the number of nickels is n.

According to the problem, Mercedese has 3 fewer dimes than nickels, which means the number of dimes is n - 3.

Additionally, she has 4 more quarters than nickels, so the number of quarters is n + 4.

Next, we need to calculate the value of the coins in cents.

The value of nickels is 5n cents,
the value of dimes is 10(n - 3) cents, and
the value of quarters is 25(n + 4) cents.

Given that Mercedese has a total of 37 coins, we can set up the equation:

n + (n - 3) + (n + 4) = 37

Now, let's solve the equation:

3n + 1 = 37
3n = 36
n = 12

Therefore, Mercedese has 12 nickels.

To find out the total value of the coins, we can substitute the value of n into the equation for each coin:

Value of nickels = 5n = 5 * 12 = 60 cents
Value of dimes = 10(n - 3) = 10 * (12 - 3) = 90 cents
Value of quarters = 25(n + 4) = 25 * (12 + 4) = 400 cents

Now, let's calculate the total value:

Total value = 60 + 90 + 400 = 550 cents

Therefore, Mercedese had $5.50 in coins.