Pradip and pam each have apple slices and orange slices. The ratio of apple slices to the total number of slices is 4 to 11. The ratio of the total number of slices to orange slices on Pam's plate is 13:6. Neither person has more than 20 total slices. Who has more slices? Explain
Pam has 13 oranges and pradip has 11oranges
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To determine who has more slices, we need to compare the number of slices each person has. Let's start by setting up equations based on the given information.
Let's assume Pradip has x apple slices and y orange slices, while Pam has a apple slices and b orange slices.
According to the given information, the ratio of apple slices to the total number of slices on Pradip's plate is 4:11. This means that:
x/(x+y) = 4/11
Similarly, the ratio of the total number of slices to orange slices on Pam's plate is 13:6. This means that:
(a+b)/b = 13/6
We also know that neither person has more than 20 total slices, so we can write:
x + y ≤ 20 (for Pradip)
a + b ≤ 20 (for Pam)
To solve this problem, we can use a method called substitution. Let's solve the equation for x/(x+y) first.
x/(x+y) = 4/11
Multiply both sides by (x+y):
x = (4/11)(x+y)
Now, let's simplify this equation:
11x = 4(x+y)
11x = 4x + 4y
7x = 4y ---- (Equation 1)
Similarly, let's solve the equation for (a+b)/b:
(a+b)/b = 13/6
Multiply both sides by b:
a + b = (13/6)b
Now, let's simplify this equation:
6(a+b) = 13b
6a + 6b = 13b
6a = 7b ---- (Equation 2)
We can now compare the number of slices each person has. Let's find the values of x and y.
From Equation 1, we have 7x = 4y. We know that x + y ≤ 20, so we can assume x = 4 and y = 3 (keeping in mind that the total cannot exceed 20).
Similarly, let's find the values of a and b.
From Equation 2, we have 6a = 7b. We know that a + b ≤ 20, so we can assume a = 6 and b = 7.
Now, let's calculate the total number of slices for each person:
Pradip: x + y = 4 + 3 = 7 slices
Pam: a + b = 6 + 7 = 13 slices
Comparing the total number of slices, we can see that Pam has more slices than Pradip.