Algebra 1 help?

Question

I get stuck on these.

Solve the proportion-

32 - y / y = 6/10

p + 15/42 = p - 5/14

2z/z + 7 = 24/54

7/2 = b + 4.5/b - 0.5

4/c + 1.8 = 6/c + 4.3

Would you mind explaining it to me >.<
I greatly appreciate it.

Answer 1

the basic trick with proportions is that if a/b = c/d, then ad = bc (cross products are equal).

(32-y)/y = 6/10
10(32-y) = 6y
320 - 10y = 6y
320 = 16y
20 = y

(p+15)/42 = (p-5)/14
14(p+15) = 42(p-5)
p + 15 = 3(p - 5)
p + 15 = 3p - 15
30 = 2p
15 = p

2z/(z+7) = 24/54
2z/(z+7) = 4/9
18z = 4(z+7)
18z = 4z + 28
14z = 28
z = 2

7/2 = (b + 4.5)/(b - 0.5)
7(b - 0.5) = 2(b + 4.5)
7b - 3.5 = 2b + 9
5b = 12.5
b = 2.5

4/(c + 1.8) = 6/(c + 4.3)
4(c + 4.3) = 6(c + 1.8)
4c + 17.2 = 6c + 10.8
6.4 = 2c
3.2 = c

Answer 2

For the first one,
I'm assuming it is (32-y)/y = (6/10)
So, (32-y) * 10 = 6y (just multiplied to get rid of fractions)
then 320 - 10y = 6y
320 = 16y
y= 20

For the second one,
again, assuming (p+15)/42 = (p-5)/14
So, 14 (p + 15) = 42 (p- 5) (i hate fractions)
then (p + 15) = 3 (p - 5) (divided both sides by 14)
p + 15 = 3p - 15
30 = 2p
p = 15

(2z/z + 7 )= 24/54
108z = 24z + 168
84z = 168
z =2

(7/2) = b + (4.5/b - 0.5)
7b - 3.5 = 2b + 9
5b = 12.5
b = 2.4

(4/c+1.8) = (6/c + 4.3)
4c + 17.2 = 6c + 10.8
2c = 6.4
c = 3.2

Answer 3

To solve these problems, you must use the following idea
a/b = c/d becomes ad=bc (multiplying both sides by the denominator of both fractions).

(32-y)/y = 6/10
10(32-y) = 6y
320-10y = 6y
320 = 16y
20 = y

(p+15)/42 = (p-5)/14
14(p+15) = 42(p-5)
14p+210 = 42p-210
420 = 28p
15 = p

2z/(z+7) = 24/54
54(2z) = 24(z+7)
108z = 24z+168
84z = 168
z = 2

7/2 = (b+4.5)/(b-0.5)
7(b-0.5) = 2(b+4.5)
7b-3.5 = 2b+9
5b = 12.5
b = 2.5

4/(c+1.8) = 6/(c+4.3)
4(c+4.3) = 6(c+1.8)
4c+17.2 = 6c+10.8
6.4 = 2c
3.2 = c

Answer 4

alright man. this stuff isn't that hard to understand.

just cross multiply. like for the first problem... y * 6 = 6y
10 * 32-y = 320 - 10y

so u have this.... 6y=320-10y. add 10y to both sides because ur trying to solve for y. so u then get 16y=320. then to get y, divide both sides by 16 which gets u y= 20.

just do that for all the other problems.

Answer 5

you just cross multiply

32 - y / y = 6/10
10 (32-y) = 6 (y)
320 - 10y = 6y
320 = 16y
y= 20

in other words, you multiply the outsides by the insides, but its easier to see when written in a fraction

Answer 6

wish i could help, but i HATED that class, Algebra 2=MUCH easier...

Answer 7

first of all i was wondering what grade you were in?