Question

14 the time t needed to complete a task varies inversely as the number of men p. it takes 5 h for seven men to install a new roof. how long does it take 10 men to complete the job? 3.5 h 15 the cost of each item bought is inversely proportional to the number of items when spending a fixed amount. when 42 items are bought, each costs $1.50. find the number of items when each costs $2.16. about 28 items

Explanation:

Step1: Define inverse proportion (Q14)

For inverse proportion, $t = \frac{k}{p}$, where $k$ is constant.

Step2: Solve for constant $k$ (Q14)

Substitute $t=5$, $p=7$:
$k = t \times p = 5 \times 7 = 35$

Step3: Calculate time for 10 men (Q14)

Substitute $p=10$, $k=35$:
$t = \frac{35}{10} = 3.5$

Step4: Define inverse proportion (Q15)

Let cost $c = \frac{k}{n}$, $n$=number of items.

Step5: Solve for constant $k$ (Q15)

Substitute $n=42$, $c=1.44$:
$k = c \times n = 42 \times 1.44 = 60.48$

Step6: Calculate number of items (Q15)

Substitute $c=2.16$, $k=60.48$:
$n = \frac{60.48}{2.16} = 28$

Answer:

1. For question 14: 3.5 h
2. For question 15: 28 items