7.RP.A.3 Tutor Intake -- Multistep Ratio and Percent Problems

Finding a new value after a percent increase -- new value = original $\times$ (1 + percent/100).

Finding a percent error -- |measured $-$ actual| / actual $\times$ 100.

Finding simple interest -- $I = prt$.

Finding the original value before a change -- original = new / (1 + percent/100).

The student divided by the new value (60) instead of the original value (50); percent change is always relative to the original.

The student should have used 10/50 x 100 but wrote the wrong numerator.

Nothing -- $10/60$ is correct because 60 is the more recent value.

The student needed to add 50 and 60 together first.

No -- the final price is $96, because the 20% decrease applies to the new price ($120), not the original $100.

Yes -- equal and opposite percents always cancel to return to the original value.

No -- but only because the percents should have been added instead of computed separately.

Yes -- as long as both percents are applied to the same original value.