Please explain in detail how to solve each question:
At a certain high school, 350 students are taking an algebra course. 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 firs step of solving the system? Why?
How can you interpret the solution in the context of the problem?
let the number of boys be 33x and the number of girls be 37x
(notice 33x : 37x = 33:37 )
33x + 37x = 350
70x = 350
x = 5
so number of boys = 33(5) = 165
number of girls = 37(5) = 185
So 20 more girls than boys take algebra
check:
notice 165+185 = 350
and 165:185 = 33:37
No need to have a system of equations here, the above is the simplest way to do ratio problems.
I suppose you could say
number of boys -- x
number of girls -- y
then x+y = 350 , or y = 350-x
also x:y = 33:37
x/y = 33/37
37x = 33y
37x = 33(350-x)
37x = 11550 - 33x
70x = 11500
x = 165
then y = 350-165 = 185
as I found much easier and faster above
Wow
Uh my tiny 8th grade mind needed to read that twice... heh... I'm slow.
I am so confused, I need more help please!!!
Well, well, well, it seems like we have some algebraic mysteries to unravel here! Fear not, for Clown Bot is here to bring laughter and solve equations at the same time.
Let's tackle the first question:
To find out how many more girls are taking algebra than boys, we need to determine the difference between the number of girls and boys. We are given that the ratio of boys to girls is 33:37, so we can use this information to set up our system of equations.
Let's say that the number of boys taking algebra is represented by 'b' and the number of girls taking algebra is represented by 'g'.
Our first equation will be:
b/g = 33/37
This equation represents the ratio of boys to girls in terms of fractions.
And our second equation will be:
b + g = 350
This equation represents the total number of students taking algebra, which is given as 350.
Now, to solve this system of equations, we can use one of two methods - substitution or elimination. Since the first question doesn't ask for the method, let's focus on the second and third questions:
In the first step of solving the system, we have a choice to make. We can solve for a variable by isolating it in one equation, and then substitute that expression into the other equation. In this case, it would be easier to solve for 'b' in terms of 'g' in the first equation:
b/g = 33/37
Cross-multiplying gives us:
37b = 33g
Now, we can solve for 'b':
b = (33/37)g
By isolating 'b' in this way, we have created an expression for 'b' in terms of 'g'. Since we have eliminated one variable, we can substitute this expression into the second equation:
(33/37)g + g = 350
Now, solve for 'g' using this equation.
Finally, to interpret the solution in the context of the problem, simply plug the value of 'g' back into the expression for 'b'. Subtract the number of boys from the number of girls to find the difference, and voila! You have the answer to how many more girls are taking algebra than boys at that high school.
Remember, solving equations can be a serious task, but don't forget to have a laugh while you do it. Good luck!
To solve the question, we need to find the number of girls and boys taking the algebra course and calculate the difference between the two.
First, let's write a system of equations to model the situation. Let's assume the number of boys taking algebra is 'x', and the number of girls taking algebra is 'y.'
From the given information, we know that the ratio of boys to girls taking algebra is 33:37. Therefore, we can write the following equation:
x/y = 33/37 ---- (Equation 1)
We also know that a total of 350 students are taking the algebra course. Hence, the sum of boys and girls taking algebra is equal to 350 students:
x + y = 350 ---- (Equation 2)
Now, we have a system of equations:
Equation 1: x/y = 33/37
Equation 2: x + y = 350
To solve the system of equations, we can use either substitution or elimination method.
Next, to find the solution, let's solve the system of equations by the substitution method:
1. Solve Equation 2 for one variable (let's solve for x):
x = 350 - y
2. Substitute the value of x in Equation 1:
(350 - y)/y = 33/37
3. Cross multiply and simplify the equation:
37(350 - y) = 33y
12950 - 37y = 33y
4. Solve for y by combining like terms:
12950 = 70y
y = 12950/70
y ≈ 185.00
So, the approximate number of girls taking algebra is 185.
Now, to find the number of boys, we substitute the value of y in Equation 2:
x + 185 = 350
x = 350 - 185
x = 165
The approximate number of boys taking algebra is 165.
To calculate the difference between the number of girls and boys taking algebra, we subtract the number of boys from the number of girls:
185 - 165 = 20.
Therefore, there are 20 more girls taking algebra than boys.
To interpret the solution in the context of the problem, we can say that out of the 350 students taking the algebra course, there are approximately 185 girls and 165 boys. Additionally, there are 20 more girls taking algebra than boys.