There are 1170 students in a school. The ration of girls to boys is 23 : 22. The system below describes..?
relationships between the number of girls and the number of boys.
g+b=1170
g/b=22/23
a. Solve the proportion for g.
b. Solve the system.
c. How many more girls are there than boys?
ratio
a. well...first you divide 1170 by 45(I got 45 by adding the amount of the ratio 23+22) and you get 26.so then you multiply 26 by 23 to get the number of girls. you mulitply 26 by 22 to get the number of boys. so G = 498
b. above
c. there are 26 more girls than boys
what's the proportion when it's solved, using g/b=22/23?
a. To solve the proportion for g, we can multiply both sides of the equation by b:
(b/g) * g = (b/g) * (22/23)
This simplifies to:
b = (22/23) * g
b. To solve the system of equations, we can substitute the expression for b from the proportion into the first equation:
g + (22/23) * g = 1170
Multiply both sides by 23 to get rid of the fraction:
23g + 22g = 1170 * 23
Combine like terms:
45g = 26910
Divide both sides by 45:
g = 26910 / 45
Simplify:
g = 598
Now that we have the value for g, we can substitute it back into the equation for b:
b = (22/23) * g
b = (22/23) * 598
Simplify:
b = 578
c. To find how many more girls there are than boys, we subtract the number of boys from the number of girls:
Number of girls - Number of boys = 598 - 578 = 20
There are 20 more girls than boys.
The given system of equations describes the relationship between the number of girls and the number of boys in the school.
Let's proceed to solve the system of equations:
a. Solve the proportion for g:
The proportion is g/b = 22/23. To solve for g, we can cross-multiply and then isolate g:
g/b = 22/23
23g = 22b
g = (22b)/23
b. Solve the system:
To solve the system, we'll use the first equation g + b = 1170 and substitute the expression for g from the proportion:
g + b = 1170
[(22b)/23] + b = 1170
To solve this equation, we can multiply through by 23 to eliminate the fraction:
23 * [(22b)/23] + 23 * b = 23 * 1170
22b + 23b = 26910
45b = 26910
Dividing both sides by 45:
b = 26910/45
b = 598
Now we can substitute this value of b back into the first equation to find g:
g + 598 = 1170
g = 1170 - 598
g = 572
So, there are 572 girls and 598 boys in the school.
c. How many more girls are there than boys?
To find the difference between the number of girls and boys, we subtract the number of boys from the number of girls:
Difference = Number of Girls - Number of Boys
Difference = 572 - 598
Difference = -26
Therefore, there are 26 more boys than girls in the school.