Answer :
Answer:
There were 69 students in advanced math and 184 students in regular math before the placement tests
Step-by-step explanation:
The correct question
At the beginning of 6th grade, the ratio of the number of advanced math students to the number of regular math students was 3:8. However, after taking placement tests, students were moved around changing the ratio of the number of advanced math students to the number of regular math students to 4:7. How many students started in regular math and advanced math if there were 92 students in advanced math after the placement tests?
Let
x ----> the number of advanced math students
y ----> the number of regular math students
we know that
At the beginning of grade 6
[tex]\frac{x}{y}=\frac{3}{8}[/tex] ----> equation A
After taking placement tests
[tex]\frac{x}{y}=\frac{4}{7}[/tex] ----> equation B
[tex]x=92[/tex] ----> equation C
Remember that
The total number of students at the beginning of grade 6 is the same that the number of students after taking placement tests
step 1
Find out the total number of students after taking placement tests
we have
[tex]\frac{x}{y}=\frac{4}{7}[/tex] ----> equation B
[tex]x=92[/tex] ----> equation C
substitute the value of x in equation B and solve for y
[tex]\frac{92}{y}=\frac{4}{7}[/tex]
[tex]y=7(92)/4\\y=161[/tex]
The total number of students after taking placement tests is
[tex]x+y=92+161=253[/tex]
step 2
Find out how many students started in regular math and advanced math
we have that
At the beginning of grade 6
[tex]\frac{x}{y}=\frac{3}{8}[/tex] ----> equation A
[tex]x+y=253[/tex] -----> equation D
Solve the system of equations by graphing
The solution is the intersection point both graphs
using a graphing tool
The solution is the point (69,184)
see the attached figure
therefore
There were 69 students in advanced math and 184 students in regular math before the placement tests
Answer: 69 kids in advanced math, 184 kids in regular math. hope it helped