at a certain high school,350 students are taking algebra. the ratio of boys to girls taking algebra is 33:37. How many more girls are taking algebra than boys?

- How can you write a system of equations to model the situation?
- Which equation will you solve for a variable in the first step of solving the system? why?
-how can you interpret the solution in the context of the problem?

easier way:

let the number of boys taking algebra be 33x
let the number of girls taking algebra be 37x

33x+37x = 350
70x = 350
x = 5

number of boys = 33(5) = 165
number of girls = 37(5) = 185

b = Boys

g = Girls

This is a systems of equations

1. b + g = 350

2. b = (33/37)g

Then, you can solve the first equation for one of the variables or substitute the second equation into the first equation for b. Then, substitute to find the number of boys. Finally, subtract the two answers to determine the difference in girls and boys taking algebra.

To model the situation, we can set up a system of equations. Let's use the variables "b" for the number of boys taking algebra and "g" for the number of girls taking algebra.

1) From the problem statement, we know that the total number of students taking algebra is 350:
b + g = 350

2) We are also given that the ratio of boys to girls taking algebra is 33:37:
b/g = 33/37

To solve this system of equations, we can use the substitution or elimination method. Let's use the substitution method for this example.

We can rearrange equation 2 to solve for b:
b/g = 33/37
Cross-multiplying, we get:
37b = 33g
Dividing both sides by 37, we have:
b = (33/37)g

Now we can substitute this expression for b into equation 1:
(33/37)g + g = 350
Multiplying through by 37 to eliminate the fraction:
33g + 37g = 12950
70g = 12950
g = 185

To find the value of b, we substitute g = 185 back into equation 1:
b + 185 = 350
b = 350 - 185
b = 165

Now, to answer the question of how many more girls are taking algebra than boys, we subtract the number of boys from the number of girls:
185 - 165 = 20

Thus, there are 20 more girls taking algebra than boys.

no of girls=37/70*350=185

no of boyz=350-185=165
185-165=20girls more dan boiz.
Let x=boys y=girls
A)x+y=350
350-((ratio of girls/total ratio)*350=no of boys taking algebra.
No of girls-no of boys=girls more dan bois.
B)u wuld use both d 2nd n 3rd eqn