In description please help!

Question

I sarah had 3 more apples, then she would have three-quarters of the number of apples that matthew has. if Sarah gave away 3 apples , then she would have half the number of apples matthew has. How many apples does sarah have?

Answer 1

Good Morning, Jake,

So, let's begin by assigning some expressions and terms to represent what has been given in the problem, fair enough?

First, let the following be true:

s = Sarah's apples

m = Matthew's apples

We good so far? Of course you are! You are a wiz when it comes to this stuff!

Second, let's write an equation and solve for both statements provided in our problem, fair enough? Great!

"If Sarah had 3 more apples, then she would have three quarters the number Matthew has."

s + 3 = 3/4m

s + 3 = 3/4m <---Multiply both sides of the equation by 4 to eliminate the fraction.

4(s + 3) = 3m <---Simplify

4s + 12 = 3m <----This is what we are left with after simplifying.

"If Sarah gave away 3 apples, then she would have half the number of apples that Matthew has."

s - 3 = 1/2m <----Multiply both side of the equation by 2 to eliminate the fraction.

2(s - 3) = m <---Simplify

2s - 6 = m <---This is what we are left with after simplifying.

Third, in the first equation substitute 2s - 6 for m, okay?

4s + 12 = 3(2s -6) <-----Simplify

4s + 12 = 6s - 18 <----Add 18 to both sides of the equation AND subtract 4s from both sides.

12 + 18 = 6s - 4s <----Simplify

30 = 2s <----Solve for s

s = 15 The number of apples Sarah has.

Sarah has 15 apples.

Let's check our work, okay? According to the problem, if "Sarah had 3 more apples, then she would have 3/4 the number of apples that Matthew has," right?

s + 3 = 3/4m

15 + 3 = 3/4m <-------Multiply both sides of the equation by 4.

4(15 +3) = 3m

60 + 12 = 3m

72 = 3m

m = 24

If Sarah, did, in fact have 3 more apples than she would have 18 apples which is precisely 3/4 of the number of apples Matthew has, therefore the solution is correct and valid.

I hope I have assisted and that you have a great Thanksgiving break. If you need further clarity to my solution, wish to leave feedback, or have further questions, please feel free to click the "add comment button and ask beneath the solution. If you need one-on-one tutoring, please feel free to contact me through the Wyzant system. Best!