Can oneone help me on this MATH SAT problem?

Question

in 1995, Dianna read 10 English books and 7 French books. In 1996, she read twice as many french books as english books. If 60% of the books that she read during the 2 years were French, how many English and French books did she read in 1996?

a. 16
b. 26
c. 32
d. 39
e. 48

Answer 1

Let b stand for the number of English books she read in 1996. Then she read 2b French books in 1996. In all, she read 7 + 2b French books and 10 + b English books, for a total of (7 + 2b) + (10 + b) = 17 + 3b books of both types. Then if 60% of them were French, we have 7 + 2b = .6(17 + 3b) = 10.2 + 1.8b.
Thus .2b = 3.2, or b = 3.2/.2 = 16.

Now let's check this.
In 1996 she read 32 French books and 16 English books.
(32 = 16 X 2)
In total she read 7 + 32 = 39 French books and 10 + 16 = 26 English books, for a total of 39 + 26 = 65 books.
(French books / total books = 39/65 = 3/5 = 60%)

So in 1996 she read a total of 32 + 16 = 48 books. The answer is e.

Answer 2

Not that difficult. Just follow the steps.

1. Say she read X english books in 2nd year. So number of french books she read is 2X. Total books read in the 2nd year is X + 2X = 3X.

2. Total french books she read in 2 years = 7 + 2X. Total English books she rad in 10 + X. Total books she read in 2 years = 17 + 3X.

3. 60% of total books she read in 2 year is french. This means 0.6 * (17 + 3X) = 7 + 2X. We need to solve this equation to get the value of X, which is the number of english books she read in 1996.

10.2 + 1.8x = 7 + 2x
or 0.2x = 3.2
or x = 16 books.

Since she read twice the number of english books are french b ooks in 1996, the number of french books she read in that year is 2*16 = 32 books.

Total number of books she read in 1996 = 16 + 32 = 48.

Hence answer is "e".

Answer 3

This is a variation on a mixture problem.

Let

E = number of English books
F = number of French books

1995

E = 10
F = 7

1996

E = a
F = 2a

For both years combined

F/(E + F) = (7 + 2a)/(10 + 7 + a + 2a) = 6/10
(7 + 2a)/(17 + 3a) = 3/5
5(7 + 2a) = 3(17 + 3a)
35 + 10a = 51 + 9a
a = 16

For 1996

E + F = a + 2a = 3a = 3(16) = 48

So the answer is e. 48.

Answer 4

take to english books she read in the 2nd yr as x &french books as y

total books she read in the two yrs is;
10+x english books
7+y french books
that is 17+x+y in total right?
60% of these are french;
i.e (17+x+y)*60%=7+y
now she read twice as many french books as english books so
2*english books=french books
2x=y

.6(17+.5y+y)=7+y
10.2+.9y=7+y
3.2=.1y
y=32
x would be 16
books read in 1996?x+y=48
So the answer would be e(48)

Answer 5

e=english...f=french
.6(10+e+7+f)=7+f
2e=f
substitute in 2e for f
.6(17+e+2e)=7+2e
.6(17)+.6(3e)=7+2e
10.2+1.8e=7+2e
-7 -1.8e -7-1.8
3.2=.2e
divide each side by.2

16=e

sub in 16 for e in 2e=f

2(16)=f
32=f

32+16=48... answer e

Answer 6

e

Answer 7

toooooooo confusing sorry......