Yesterday, Lucy had n apples. Today she bought 4 new apples but used a third of the total to make a pie.
How many apples does she have now?
The total number of apples is:
n+4
To make the pie, Lucy used the following number of apples:
\dfrac{n+4}{3}
The number of apples that remain is:
\left(n+4\right) - \dfrac{n+4}{3}
We need to simplify this expression:
n+4- \dfrac{n+4}{3} = \dfrac{3n+12 -n-4}{3}=\dfrac{2n+8}{3}
Lucy has now \dfrac{2n+8}{3} apples.
Paul is n years old. In five years, Emma will be three times as old as Paul.
How old is Emma now?
Assume that Emma is m years old. According to the hypothesis of the question, we have:
m+5 =3\left(n+5\right)\Rightarrow m+5 = 3n+15 \Rightarrow m=3n + 10
The age of Emma is:
3n+10
Louise had n dollars yesterday. She bought a purse with \dfrac{1}{5} of her money. Then, she went to a bookshop and bought some books using \dfrac{2}{3} of the remainder of her money.
How much money does she have now?
The amount of money Louise paid for the purse is:
\dfrac{n}{5}
Before arriving to the bookshop, she had:
n-\dfrac{n}{5} = \dfrac{4n}{5}
The amount of money she paid for the books equals:
\dfrac{2}{3} \times \dfrac{4n}{5} = \dfrac{8n}{15}
Therefore, what remains is:
\dfrac{4n}{5} - \dfrac{8n}{15} = \dfrac{12n-8n}{15} = \dfrac{4n}{15}
Louise has now \dfrac{4n}{15} dollars.
Chloe had n books. She lost one of the books and read two thirds of the remaining books. What is the number of books Chloe has not read?
Since she has lost one book, the number of remaining books equals:
n-1
She has read two third of them. That is:
\dfrac{2}{3} \left(n-1\right)
The number of books that she has not read equals:
n-\dfrac{2}{3}\left(n-1\right) = n - \dfrac{2}{3}n + \dfrac{2}{3} = \dfrac{n+2}{3}
The number of books that Chloe has not read is:
\dfrac{n+2}{3}
What is the sum of five times a number n and one third of its half?
We have:
5n+ \dfrac{1}{3} \times n \times \dfrac{1}{2} = 5n+\dfrac{n}{6}
The sum of five times a number and one third of its half is 5n+\dfrac{n}{6}
Paul and Luise have n cards in total. Paul has 4 cards less than three times as many as Louise.
How many cards does Paul have?
Suppose that Louise has m cards. The number of Paul's cards equals:
3 m-4
On the other hand, the total number of cards is n. Hence:
m + 3 m-4=n \Rightarrow 4 m=n+4 \Rightarrow m= \dfrac{n+4}{4}
Therefore, the number of cards is equal to:
n-\dfrac{n+4}{4} = \dfrac{4n-n-4}{4}= \dfrac{3n-4}{4}
The number of cards equals:
\dfrac{3n-4}{4}
Adam has a full jug of lemonade. He fills a glasses, which have a capacity of 0.2 liter each, and the jug remains \dfrac{3}{8} full.
How much is the capacity of the jug in terms of a ?
Assume that the capacity of the jug is n liters. We have:
\left(1-\dfrac{3}{8}\right)n = a \times 0.2 \Rightarrow \dfrac{5}{8}n =a \times 0.2 \Rightarrow n=\dfrac{8\times 0.2 \times a}{ 5}=0.32a
The capacity of the jug is:
0.32 a