At the beginning of grade 6, the ratio of number of advanced math students to the number of regular math students was 3:8. However, after taking placement tests common students were moved around changing the ratio of the number of advanced math students to the number of regular math students for the 7:8. How many students started regular math and advanced math if there are 92 students in regular math and advanced math after taking placement tests?

Answer:There were 69 students in advanced math and 184 students in regular math before the placement testsStep-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?Letx ----> the number of advanced math studentsy ----> the number of regular math studentswe know thatAt the beginning of grade 6[tex]\frac{x}{y}=\frac{3}{8}[/tex] ----> equation AAfter taking placement tests[tex]\frac{x}{y}=\frac{4}{7}[/tex] ----> equation B[tex]x=92[/tex] ----> equation CRemember thatThe total number of students at the beginning of grade 6 is the same that the number of students after taking placement testsstep 1Find out the total number of students  after taking placement testswe have[tex]\frac{x}{y}=\frac{4}{7}[/tex] ----> equation B[tex]x=92[/tex] ----> equation Csubstitute 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 2Find out how many students started in  regular math and advanced mathwe have thatAt the beginning of grade 6[tex]\frac{x}{y}=\frac{3}{8}[/tex] ----> equation A[tex]x+y=253[/tex] -----> equation  DSolve the system of equations by graphingThe solution is the intersection point both graphsusing a graphing toolThe solution is the point (69,184)see the attached figurethereforeThere were 69 students in advanced math and 184 students in regular math before the placement tests