Mr Leon spent $60 on some apples, mangoes and pears in the ratio 3:5:2. The number of apples was twice the number of mangoes. The number of pears was 1/3 the number of apples. The mangoes were at 3 for $5. How many fruits did he buy altogether?
The cost of the x mangoes is 5/3 x so the costs are in the ratio
5x : 5/3 x : 10/3 x
5x + 5/3 x + 10/3 x = 60
x = 6
If there were a,m,p of each fruit, respectively, then
a = 2m
3a = p
so a:m:p = 2:1:6
now, knowing there were 6 mangoes, we have
12+6+36 = 54 fruits
amount spent on apples --- $ 3x
amount spent on mangoes -- $ 5x
amount spent on pears ---$ 2x
3x+5x+2x = 60
x = 6
"The mangoes were at 3 for $5", but he spent 5x or $30 on mangoes
at 3 for $5, there must have been 18 mangoes.
number of
apples : pears : mangoes = 2y : 2y/3 : y
= 6y : 2y : 3y
But we know the number of mangoes is 18
so 3y = 18, y = 6
so we have 36 apples, 12 pears and 18 mangoes
check:
twice as many apples as mangoes ?? Yes
The number of pears was 1/3 the number of apples ?? , YES
I think oobleck has the number of apples as 1/3 the number of pears, should be the other way around.
To solve this problem, we'll first find the number of mangoes Mr. Leon bought.
Given that the price of mangoes is 3 for $5, we can conclude that each mango costs $5/3. Let's assume Mr. Leon bought x mangoes.
So, the cost of the mangoes he bought would be x * ($5/3).
Next, we're told that the number of apples is twice the number of mangoes. Hence, the number of apples he bought would be 2x.
Similarly, the number of pears is 1/3 the number of apples. Thus, the number of pears he bought would be (1/3) * (2x), or 2x/3.
Now, considering the given ratio of 3:5:2, the total number of fruits bought can be expressed as 3x + 5x + (2x/3).
To find the total cost, we know that Mr. Leon spent $60 on fruits.
So, we need to calculate the cost of each fruit using the given ratio and the total cost.
The ratio of apples to mangoes to pears is 3:5:2, which simplifies to 9:15:6.
To calculate the cost per fruit, we divide the total cost by the sum of the ratios: $60 / (9 + 15 + 6) = $60 / 30 = $2.
Now, we have the cost per fruit ($2) and the total number of fruits, 3x + 5x + (2x/3).
Setting up the equation, we can solve for x:
2 * (3x) + 2 * (5x) + 2 * (2x/3) = $60
6x + 10x + 4x/3 = $60
Multiplying through by 3 to eliminate the fraction:
18x + 30x + 4x = $180
52x = $180
x = $180 / 52
x ≈ 3.46
Since we can't have a fraction of a fruit, we'll round x to the closest whole number, in this case, 3.
So, Mr. Leon bought 3 mangoes.
Now, let's calculate the number of apples and pears using the values we've found.
Number of apples = 2x = 2 * 3 = 6
Number of pears = 2x/3 = (2 * 3)/3 = 2
Finally, to determine the total number of fruits, we add up the number of apples, mangoes, and pears:
Total number of fruits = Number of apples + Number of mangoes + Number of pears
Total number of fruits = 6 + 3 + 2 = 11
Therefore, Mr. Leon bought a total of 11 fruits.