The prices of noodle set and rice set at two shops are shown below.

((a))
Find $\displaystyle \begin{pmatrix}2.5 & 3.5\\[4pt]2.8 & 3.2\end{pmatrix}\begin{pmatrix}2\\[4pt]1\end{pmatrix}$ .

Answer ___
((b))
Describe what your answer in (a) represents.
((c))
Sally has to buy a total of 6 meal sets from one particular shop.
How many noodle sets and rice sets does she have to buy such that the total cost is the same regardless of whether she buys from Shop R or Shop S?

Answer ___ noodle set(s), ___ rice set(s)

Sum product Interpreting matrix Formulating equations Calculator Display matrix Letters represent numbers Translation real world Linear one variable 中文

Work through it with AI →

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

22((a))

1. Multiply each row of the matrix by the column vector.

\begin{pmatrix}2.5 & 3.5\\2.8 & 3.2\end{pmatrix}\begin{pmatrix}2\\1\end{pmatrix} = \begin{pmatrix}2.5(2)+3.5(1)\\2.8(2)+3.2(1)\end{pmatrix}

2. Evaluate the two entries of the resulting column vector.

\begin{pmatrix}2.5(2)+3.5(1)\\2.8(2)+3.2(1)\end{pmatrix} = \begin{pmatrix}5+3.5\\5.6+3.2\end{pmatrix} = \begin{pmatrix}8.5\\8.8\end{pmatrix}

Answer

$\begin{pmatrix}8.5\\8.8\end{pmatrix}$

22((b))

1. Identify what the column vector represents.

The column vector $\begin{pmatrix}2\\1\end{pmatrix}$ means $2$ noodle sets and $1$ rice set.

2. Interpret the two entries of the answer from part (a).

From part (a), $\begin{pmatrix}8.5\\8.8\end{pmatrix}$ corresponds to the total costs at the two shops. The first entry is for Shop R and the second entry is for Shop S.

Answer

The answer represents the total cost of buying $2$ noodle sets and $1$ rice set from each shop: $8.50 from Shop R and $8.80 from Shop S.

22((c))

1. Define variables and express the total cost at each shop.

Let the number of noodle sets be $x$ .

Since Sally buys a total of $6$ meal sets, the number of rice sets is $6-x$ .

Cost at Shop R:
$2.50x+3.50(6-x)$
Cost at Shop S:
$2.80x+3.20(6-x)$

2. Equate the two costs and solve for the number of noodle and rice sets.

For the total cost to be the same,
$2.50x+3.50(6-x)=2.80x+3.20(6-x)$
$2.50x+21-3.50x=2.80x+19.20-3.20x$
$21-x=19.20-0.40x$
$1.80=0.60x$
$x=3$

So Sally buys $3$ noodle sets and $6-3=3$ rice sets.

Answer

$4$ noodle set(s), $2$ rice set(s)

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.

The prices of noodle set and rice set at two shops are shown below.

Worked solution

22((a))

22((b))

22((c))

More questions on this topic