Question

4 the weight of a box of nails and a box of screws is 2.5 kg. four boxes of nails and a box of screws weigh 7 kg. determine the weight of each.

5 an enclosure at a wildlife sanctuary contains wombats and emus. if the number of heads totals 28 and the number of legs totals 88, determine the number of each species present.

Explanation:

Define variables for Question 4

Using the Linear Equations knowledge point
Let \(n\) be the weight of a box of nails in kg.
Let \(s\) be the weight of a box of screws in kg.

Set up and solve the system for Question 4

Using the Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Subtract the first equation from the second:

$$ 3n = 4.5 \implies n = 1.5 $$

Substitute \(n = 1.5\) back into the first equation:

$$ 1.5 + s = 2.5 \implies s = 1 $$

Define variables for Question 5

Using the Linear Equations knowledge point
Let \(w\) be the number of wombats.
Let \(e\) be the number of emus.

Set up and solve the system for Question 5

Using the Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Divide the second equation by 2:

$$ 2w + e = 44 $$

Subtract the first equation from this result:

$$ w = 16 $$

Substitute \(w = 16\) back into the first equation:

$$ 16 + e = 28 \implies e = 12 $$

Answer:

Question 4

A box of nails weighs \(1.5\text{ kg}\) and a box of screws weighs \(1\text{ kg}\).

Question 5

There are \(16\) wombats and \(12\) emus present.