8.2.2 Basic Measurements, PT3 Practice

Question 6:
The mass of a box containing 6 papayas is 21.32 kg. The mass of the box when it is empty is 1.46 kg.
Calculate the average mass, in g, of a papaya.

Solution:
Mass of 6 papayas
= 21.32 – 1.46
= 19.86 kg

Average mass of a papaya
= 19.86 ÷ 6
= 3.31 kg
= 3.31 × 1000 g
= 3310 g

Question 7:
Louis bought 600 g of cookies. Dennis bought twice the mass of cookies that Jackson bought. They bought 1.35 kg of cookies altogether. Calculate the mass, in g, of cookies bought by Jackson.

Solution:
Let Jackson bought w g of cookies.
600 g + 2 × w + w = 1.35 kg
600 g + 3w = 1.35 kg
600 g + 3w = 1350 g
3w = 1350 g – 600 g
w = 750 g ÷ 3
w = 250 g

Question 8:
If the mass of 4 packets of candies is 2.6 kg, what is the mass of 9 packets of the same candies, in kg?

Solution:
$\begin{array}{l}\text{Mass of 4 packets of candies = 2}\text{.6 kg}\\ \text{Mass of 9 packets of candies}=\frac{2.6}{4}\times 9\\ =5.85\text{ kg}\end{array}$

Question 9:
It is given that $\frac{1}{4}$ of fruits is supplied to Juice Stall A and $\frac{2}{7}$ to Juice Stall B. The remaining 133.25 kg is sold to a fruit stall.
Calculate the mass of fruits that has been supplied to Fruit Stall B.

Solution:
$\begin{array}{l}\frac{1}{4}+\frac{2}{7}=\frac{7}{28}+\frac{8}{28}\\ =\frac{15}{28}\\ \text{Remaining fruits sold to fruit stall}\\ =1-\frac{15}{28}\\ =\frac{13}{28}\\ \\ \text{Total mass of fruits}\\ =\frac{28}{13}\times 133.25\\ =287\text{ kg}\\ \\ \text{Mass of fruits supplied to Juice Stall }B\\ =\frac{2}{7}\times 287\\ =82\text{ kg}\end{array}$

Question 10:
The mixture of metal to produce a piece of 50 sen coin are $\frac{2}{3}\text{ zinc, }\frac{1}{5}\text{ nickel}$ and the rest is copper.
If the mass of copper is 1.6 g, find the total mass, in g, of zinc and nickel.

Solution:
$\begin{array}{l}\text{Fraction of copper}\\ =1-\frac{2}{3}-\frac{1}{5}\\ =\frac{15}{15}-\frac{10}{15}-\frac{3}{15}\\ =\frac{2}{15}\\ \\ \text{Portion of copper = 2 g}\\ \text{Portion of zinc and nickel = 13 g}\\ \\ 2\leftrightarrow 1.6\text{ g}\\ \text{Total mass of zinc and nickel},\\ 13\leftrightarrow \frac{13\times 1.6}{2}=10.4\text{ g}\end{array}$