A fruit stand carries apples, oranges, lemons, and pears. There are twice as many apples as oranges and 3 times as many lemons as pears. If there are 3 more oranges than pears, and p represents the number of pears, which of the following expressions represents the total number of fruits at the fruit stand?
3P
5P-5
5P
6P-1
7P+9
A=2O
L=3P
O-P=3
A+O+L+P
=2O+O+3P+P
=2(P+3)+(P+3)+3P+P
=2P+P+3P+P + 2*3+3
=?
7P+9
Let's break down the given information:
- There are twice as many apples as oranges.
- There are 3 times as many lemons as pears.
- There are 3 more oranges than pears.
Now let's express the number of each fruit in terms of p (the number of pears):
- Apples = 2 * Oranges
- Lemons = 3 * Pears
- Oranges = Pears + 3
To find the total number of fruits at the fruit stand, we need to add up all the fruits:
Total number of fruits = Apples + Oranges + Lemons + Pears
= (2 * Oranges) + Oranges + (3 * Pears) + Pears
= 2 * Oranges + Oranges + 3 * Pears + Pears
= 3 * Oranges + 4 * Pears
Now let's express the total number of fruits using the given expression options:
A. 3P --> This expression only accounts for pears, not the other fruits.
B. 5P-5 --> This expression is missing the oranges.
C. 5P --> This expression is missing the oranges and lemons.
D. 6P-1 --> This expression is missing the lemons.
E. 7P+9 --> This expression includes all the fruits, so it represents the total number of fruits at the fruit stand.
Therefore, the correct expression that represents the total number of fruits at the fruit stand is 7P+9.
To find the total number of fruits at the fruit stand, we need to determine the number of each type of fruit and then add them together.
Given the information provided:
- There are twice as many apples as oranges: apples = 2 * oranges.
- There are 3 times as many lemons as pears: lemons = 3 * pears.
- There are 3 more oranges than pears: oranges = pears + 3.
To represent the total number of fruits, we need to add up the quantities of each type of fruit: apples + oranges + lemons + pears.
Substituting the given relationships, the total number of fruits can be expressed as:
(2 * (pears + 3)) + (pears + 3) + (3 * pears) + pears
Simplifying the expression:
2pears + 6 + pears + 3 + 3pears + pears
Combining like terms:
7pears + 6 + 3 + pears
Combining constant terms:
7pears + 9
Therefore, the expression that represents the total number of fruits at the fruit stand is 7P + 9.