A vendor. Sold 2/5 of fruits to motorists and 1/4 to students. He also sold 3/7 of the remaining fruits to others. If the vendor was left with 168 fruits, how many fruits were sold to students?
Let's solve this problem step-by-step.
Step 1: Let's assume the total number of fruits initially was x.
Step 2: The vendor sold 2/5 of the fruits to motorists, which is (2/5)x.
So, the remaining fruits after selling to motorists will be: x - (2/5)x = (3/5)x.
Step 3: The vendor sold 1/4 of the remaining fruits to students, which is (1/4) * (3/5)x = (3/20)x.
So, the remaining fruits after selling to students will be: (3/5)x - (3/20)x = (9/20)x.
Step 4: The vendor sold 3/7 of the remaining fruits to others, which is (3/7) * (9/20)x = (27/140)x.
So, the remaining fruits after selling to others will be: (9/20)x - (27/140)x = (45/140)x.
Step 5: According to the question, the vendor was left with 168 fruits, which is (45/140)x = 168.
Step 6: Multiply both sides of the equation by 140 to get rid of the fraction: (45/140)x * 140 = 168 * 140.
Simplifying further, (45/140) * 140 cancels out, leaving x = 168 * 140 / 45.
Step 7: Calculate the value of x: x = 588.
Step 8: Now, substitute the value of x into the expression for fruits sold to students: (3/20)x = (3/20) * 588.
Step 9: Calculate the value of (3/20) * 588: (3/20) * 588 = 3 * 29.4 = 88.2.
Therefore, the vendor sold 88 fruits to students.
To solve this problem, we need to calculate the number of fruits sold to students. Let's break down the information given step by step:
Step 1: Calculate the fraction of fruits sold to motorists:
The vendor sold 2/5 of the fruits to motorists. To find out how many fruits were sold to motorists, we'll multiply the total number of fruits by this fraction:
2/5 * Total number of fruits = Number of fruits sold to motorists
Step 2: Calculate the fraction of fruits sold to students:
The vendor sold 1/4 of the fruits to students. Again, we'll multiply the total number of fruits by this fraction:
1/4 * Total number of fruits = Number of fruits sold to students
Step 3: Calculate the fraction of remaining fruits sold to others:
After selling fruits to both motorists and students, the vendor is left with some fruits. The problem states that the vendor sold 3/7 of the remaining fruits to others. So, we'll calculate the number of fruits sold to others by multiplying the remaining fruits by this fraction:
3/7 * Remaining fruits = Number of fruits sold to others
Step 4: Use the given information to form an equation and solve for the total number of fruits:
The problem states that the vendor was left with 168 fruits after all the sales. We can write this information as an equation:
Total number of fruits - (Number of fruits sold to motorists + Number of fruits sold to students + Number of fruits sold to others) = 168
Now, let's solve this equation to find the number of fruits sold to students.
Note: Since we don't know the total number of fruits, we'll assume it as "x" for now.
x - (2/5 * x + 1/4 * x + 3/7 * (x - (2/5 * x + 1/4 * x))) = 168
Simplifying the equation, we get:
x - (2/5 * x + 1/4 * x + 3/7 * (x - (2/5 * x + 1/4 * x))) = 168
x - (2/5 * x + 1/4 * x + 3/7 * (35/35 * x - (2/5 * x + 1/4 * x))) = 168
x - (2/5 * x + 1/4 * x + 3/7 * (35/35 * x - (8/20 * x + 5/20 * x))) = 168
x - (2/5 * x + 1/4 * x + 3/7 * (35/35 * x - (13/20 * x))) = 168
x - (2/5 * x + 1/4 * x + 3/7 * (20/20 * x - (13/20 * x))) = 168
x - (2/5 * x + 1/4 * x + 3/7 * (7/20 * x)) = 168
x - (2/5 * x + 1/4 * x + 3/20 * x) = 168
x - (16/40 * x + 10/40 * x + 12/40 * x) = 168
x - (38/40 * x) = 168
x - (19/20 * x) = 168
(20/20 * x) - (19/20 * x) = 168
(1/20 * x) = 168
x = 168 * (20/1)
Solving this equation:
x = 168 * 20
x = 3360
Therefore, the total number of fruits is 3360.
Now, we can substitute this value back into the equation for the number of fruits sold to students:
Number of fruits sold to students = 1/4 * Total number of fruits
Number of fruits sold to students = 1/4 * 3360
Number of fruits sold to students = 840
So, the vendor sold 840 fruits to students.
find the common denominator
8/20 f + 5/20 f + (3/7 * 7/20 f) + 168 = f
solve for f , 1/4 f was sold to students