Page 48 - 新思维数学学生用书9 样章

2.6 Deriving and using formulae

If you know the values of v, u and a in the formula v = u + at and you want to work v = u + at

out the value of t, you would rearrange the equation as shown. u + at = v
This makes t the subject of the formula.
at = v – u
t = v − u
a

Worked example 2.6

a Each day, Li is paid a fixed wage W dollars, and an extra R dollars per hour he works.
Write a formula for the total pay, P dollars, Li earns when he works H hours one day.
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b Use the formula in part a to work out P when W = 60, H = 8 and R = 4.80.
4
c Rearrange the formula in part a to make H the subject.
d Use your answer to part c to work out H when P = 91, W = 65 and R = 5.20.

Answer

a P = W + HR pay (P) = fixed wage (W)
+ number of hours (H) × rate of pay (R)

Remember to write H × R as HR.
b P = 60 + 8.25 × 4.80 Substitute W = 60, H = 8.25 and R = 4.80 into the formula.
= $99.60 Work out the answer and remember the units ($).

c PW = HR To make H the subject, use inverse operations.
−
Start by subtracting W from P.

P − W =
R H Now divide by R.

H = P − W Now rewrite the formula with H as the subject on the left-
R
hand side.

d H = 91 − 65 Substitute P = 91, W = 65 and R = 5.20 into the formula.
520
.
= 5 hours Work out the answer and remember the units (hours).

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