Mrs. Klein made some tarts. She sold three fifths of them in the morning and one fourth the remainder in the afternoon. If she sold 200 more tarts in the morning than in the afternoon how many tarts did she make?
number of tarts ---- x
number sold in morning = 3x/5
leaving 2x/5
number sold in afternoon = (1/4)(2x/5) = x/10
3x/5 = x/10 + 200
times 10
6x = x + 2000
5x = 2000
x = 400
check:
sold in morning = (3/5)(400) = 240
leaving 160
she sold 1/4 of 160 or 40 in the afternoon
Did she sell 200 more in the morning? YES
Answer is correct!
Let's break down the information given and solve the problem step-by-step.
Step 1: Let's assume the total number of tarts made by Mrs. Klein is "x".
Step 2: Mrs. Klein sold three-fifths of the tarts in the morning. This means she sold (3/5)x tarts in the morning.
Step 3: The remaining tarts after the morning sale can be calculated by subtracting the morning sale from the total number of tarts: (x - (3/5)x) = (2/5)x.
Step 4: Mrs. Klein sold one-fourth of the remaining tarts in the afternoon. This means she sold (1/4) * (2/5)x = (1/10)x tarts in the afternoon.
Step 5: According to the given information, she sold 200 more tarts in the morning than in the afternoon. Therefore, (3/5)x - (1/10)x = 200.
Step 6: Let's solve the equation from step 5 for x, the total number of tarts.
(3/5)x - (1/10)x = 200
Multiplying each term by 10 to eliminate the fractions:
6x - x = 2000
Simplifying the equation gives:
5x = 2000
Dividing both sides of the equation by 5:
x = 400
So, Mrs. Klein made a total of 400 tarts.
To find the number of tarts Mrs. Klein made, we'll work through the problem step by step. Let's denote the total number of tarts she made as "x".
First, Mrs. Klein sold three fifths of the tarts in the morning. This means she sold (3/5) * x tarts in the morning.
Next, she sold one fourth of the remaining tarts in the afternoon. The remainder after the morning sales is (2/5) * x. Therefore, she sold (1/4) * (2/5) * x tarts in the afternoon.
We also know that she sold 200 more tarts in the morning than in the afternoon. So, we can write the equation:
(3/5) * x = (1/4) * (2/5) * x + 200
Now, let's solve this equation to find the value of x, which represents the total number of tarts Mrs. Klein made.
Multiplying both sides of the equation by 20 to eliminate the fractions, we have:
12x = 4x + 4000
Subtracting 4x from both sides:
8x = 4000
Finally, dividing both sides by 8:
x = 500
Therefore, Mrs. Klein made 500 tarts in total.