Question

how to set this up and solve for it?

the ratio of men to women on a bus was 5/7. Then two women and one man boarded, and the ration was 7/10. How many men and women were on the bus before the last three passengers boarded?

Answer 1

@phi

Answer 2

@robtobey

Answer 3

first step, label the number of men x and women y
the ratio of men to women on a bus was 5/7 means
\[ \frac{x}{y}= \frac{5}{7} \]

Then two women and one man boarded
Now how many men do we have? How many women do we have?

Answer 4

1/2=5/7 so we would have 10 women and 7 men

Answer 5

I am sure you know ½ does not equal 5/7

think like this: I start with x men. One man boards the bus. There is now x plus ? men on board ?

Answer 6

i know what i did was multiply them to get 7/10

Answer 7

do you see we have x+1 men on board ?
now how many women ?

Answer 8

y+2

Answer 9

for women

Answer 10

Then two women and one man boarded, and the ratio was 7/10.

and what ratio can we set up ? (x+1)/(y+2) = ?

Answer 11

you should get
\[ \frac{x+1}{y+2}= \frac{7}{10} \]
cross multiply to get
\[ 10x +10= 7y+14 \\
10x -7y= 4 \]

you also have the original ratio
\[ \frac{x}{y}= \frac{5}{7}\\
7x= 5y\\
7x-5y=0\]

you have 2 equations and 2 unknowns
\[ 7x-5y=0\\10x -7y= 4\]
can you solve for x and y ?

Answer 12

sorry i had to do something

Answer 13

yes i can solve for this...

Answer 14

i would get 20 for x amount of men and 28 y amount of women
x=20,y=28

Answer 15

and 20/28 simplifies (divide top and bottom by 4) to 5/7 which matches the question
add 1 man and 2 women to get
21/30 which simplifies to 7/10.
The numbers make sense.

Answer 16

yes