Amanda and Joe have some books in the ratio 3:7. Amanda has 72 less books than Joe. How many books must Joe give to Amanda so that they will have the same number of books?
A/J= 3/7
A + 72 = J
so
A / (A+72) = 3/7
7 A = 3 A + 3*72
4 A = 3* 6*12
A = 3*6*3 = 54
J = 54+72 = 126
sum = 180
so each has 90
126 = 90 = 36
Amanda's books --- 3x
Joe's books ---- 7x
7x - 3x = 72
4x = 72
take it from here
I mean 126 - 90 = 36
To solve this problem, let's assign variables and set up equations for each person.
Let's say the number of books Amanda has is "3x" and the number of books Joe has is "7x". According to the given information, Amanda has 72 less books than Joe, so we can set up the equation:
7x - 3x = 72
Simplifying this equation, we have:
4x = 72
Now we can solve for x by dividing both sides of the equation by 4:
x = 72 / 4
x = 18
Now that we know the value of x, we can find the number of books each person has. Amanda has 3x = 3 * 18 = 54 books, and Joe has 7x = 7 * 18 = 126 books.
To find out how many books Joe must give to Amanda so that they will have the same number of books, we need to find the difference between their number of books and divide it by 2, as the difference needs to be divided equally between them.
Difference = 126 - 54 = 72
Number of books Joe must give to Amanda = Difference / 2 = 72 / 2 = 36
Therefore, Joe must give 36 books to Amanda so that they will have the same number of books.