Please help, I don’t understand

Question

Elsa has less than 40 apples. if she gave 5 apples to each of her friends, she will have 3 apples left. if she gave 7 apples to each of her friends, she will shorts of 2 apples. How many apples does Elsa have?

Answer 1

You can solve this is several ways. One way is to think it through in terms of remainder. The first statement means that the number must end in 3 more than 5 or 0: It must end in 3 or 8. You can list the numbers (3,8,13,18,23,28,33,38). The second statement says that the remainder is 2 when dividing by 7. This get your to 23.

Answer 2

5x + 3 = y - 5 apples to x # of friends + 3 remainder = total apples

7x - 2 = y - 7 apples to x # of friends - 2 apples short = total apples

x = number of friends

y = number of apples

The "+3" and "-2" represent the apples remaining or apples short in the end.

Both equations are equivalent to each other by the transitive property (a = b, b = c, therefore a = c)

5x + 3 = 7x - 2

add 2 to both sides

5x + 5 = 7x

subtract 5x from both sides

5 = 2x

x = 2.5 friends

If we put 2.5 in for x, that gives us "y = 15.5 apples."

This does not make much sense, as you cannot have half a friend.

Answer 3

Elsa has less than 40 apples. if she gave 5 apples to each of her friends, she will have 3 apples left. if she gave 7 apples to each of her friends, she will shorts of 2 apples. How many apples does Elsa have?

Let's make some equations and variables. We use our variables to represent what we don't know. The number of apples Elsa has is represented as "E" and the number of friends Elsa has is F. We know that Elsa has less than 40 apples, so E<40. E - 5*F = 3 gives the equation for "if she gave 5 apples to each of her friends, she will have 3 apples left". E - 7*F = -2 (negative 2 represents being short of 2 apples) represents the phrase " if she gave 7 apples to each of her friends, she will shorts of 2 apples". When we solve this system of equations, we get F = 2.5 and E = 15.5. You cannot have half a friend. Nevertheless, the answer would be 15.5 apples.