Joan originally had twice as many books as Emily. After she gave Emily 5 books, Joan still had 10 more than Emily. How many books did Joan have originally?
2007-07-23 13:27:05 · 7 answers · asked by wu_4533 2 in Science & Mathematics ➔ Mathematics
fourty.
2007-07-23 13:35:50 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Let j = the number of books Joan had originally
Let e = the number of books Emily had originally
j = 2e
j - 5 = (e + 5) + 10
Explanation: Joan had twice as much as Emily; that's obvious. The second equation is tricky. The negative 5 represents Joan GIVING away 5 books. Emily takes those 5, so she GETS those, so we add it. Then, it says when that giving and taking happens, Emily still has 10 less (Joan having 10 more and Emily have 10 less mean the same thing).
Plug 2e into the second equation for j.
2e - 5 = e + 5 + 10
e = 20
Emily originally had 20 books, but it wants to know how many Joan had originally.
j = 2e
j = 2(20)
j = 40
Joan originally had 40.
Check it now.
--- Is 40 twice as much as 20? Yes. Check.
--- If Joan gives away 5, she will have 35. If Emily gets 5 from Joan, she will have 25. Is 35, ten more than 25? Yes. Check.
2007-07-23 20:35:36 · answer #2 · answered by its_victoria08 6 · 0⤊ 0⤋
40.
Joan started with 40, Emily with 20. After Joan gave away 5, Joan had 35 and Emily had 25.
2007-07-23 20:30:38 · answer #3 · answered by camof2009 2 · 0⤊ 1⤋
x = Emily's books at first
2x = Joan's books at first
2x-5 = emily's books after giving 5 to Joan
x+5 = Joan's books after receiving 5 from emily
2x-5 = x+5+10
2x-5 = x +15
x = 15+5 = 20 = Emily's books at first
2x = 2*20 = 40 = Joan's books at first
2007-07-23 20:40:20 · answer #4 · answered by ironduke8159 7 · 1⤊ 0⤋
Let x denote the number of books Emily had.
Then Joan had 2x books. 2x-5 after she gave 5 books to Emily.
2x-5 = x+10 (10 more than Emily)
2x-x-5=x-x+10
x-5=10
x=15 (Emily had)
So, Joan had 2(15)=30 books (Answer)
Check: After giving 5 to Emily Joan had 25 books. Is it 10 more than Emily's 15? yes.
2007-07-23 20:37:49 · answer #5 · answered by cidyah 7 · 0⤊ 0⤋
joan had 40 books
<3
2007-07-23 20:30:49 · answer #6 · answered by Anonymous · 0⤊ 1⤋
X = original number of Emily's books
2X = original number of Joan's books
2X - 5 = X + 10
X = 15
2X = 30 (answer)
.
2007-07-23 20:36:43 · answer #7 · answered by Wise@ss 4 · 0⤊ 0⤋
Let the no of book of Emily be originally x
Therefore,Joan originally had 2x books
By the problem,
2x-5=x+5+10
or 2x-x=5+10+5
or,x=20
Hence Joan had originally 2*20 or 40 books
2007-07-23 20:33:45 · answer #8 · answered by alpha 7 · 0⤊ 0⤋
40
2007-07-23 20:31:04 · answer #9 · answered by Anonymous · 0⤊ 2⤋
She had 40 to start.
that means her friend had 20.
She gave her 5 and now she was 35 and her friend has 25.
She still has 10 more than her friend
2007-07-23 20:32:09 · answer #10 · answered by Eric A 1 · 0⤊ 1⤋