Math

Question Solve for variable QQ in the linear equation M=74Q+35M=\frac{7}{4}Q+35.

Studdy Solution

STEP 1

Assumptions
1. The equation given is M=74Q+35M=\frac{7}{4} Q+35
2. We are asked to solve for QQ

STEP 2

First, we need to isolate QQ on one side of the equation. We can do this by subtracting 35 from both sides of the equation.
M35=74QM - 35 = \frac{7}{4} Q

STEP 3

Now, to isolate QQ, we need to divide both sides of the equation by 74\frac{7}{4}. However, dividing by a fraction is the same as multiplying by its reciprocal. So we multiply both sides by 47\frac{4}{7}.
Q=47(M35)Q = \frac{4}{7} (M - 35)

STEP 4

Now, we have isolated QQ and expressed it in terms of MM. This is the solution for QQ.
Q=47M47×35Q = \frac{4}{7} M - \frac{4}{7} \times 35

STEP 5

Now, we simplify the equation by multiplying 47\frac{4}{7} with 35.
Q=47M20Q = \frac{4}{7} M - 20
So, the solution for QQ in terms of MM is Q=47M20Q = \frac{4}{7} M - 20.

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