The Edexcel Carrot and Tomato Question

Edexcel - The Carrot and Tomato Question

Well, in 2022, we had the Three Circles and this year, the Edexcel non-calculator exam perplexed students by throwing vegetables into the mix!

The sneaky Edexcel carrot and tomato question could be answered in a couple of different ways but the most simple way is by using simultaneous equations. That doesn’t mean it’s simple though, as it uses an unusual format. So, let’s a take a look at the question and its solution!

The Question

7kg of carrots and 5kg of tomatoes costs 480p.
cost of 1kg of carrots : cost of 1kg of tomatoes = 5:9
Work out the cost of 1kg of carrots and 1kg of tomatoes.

The Answer

Let’s start by looking at the first sentence in the question. This isn’t an uncommon way for a question to present information that we need to use to form an equation.

Let \(c\) be the cost of 1kg of carrots and \(t\) be the cost of 1kg of tomatoes. Then, we can form this equation:

\[7c + 5t = 480\]

Next, let’s look at the ratio on the second line. Using the same variables, \(c\) and \(t\), we can express the ratio as:

\[c:t = 5:9\]

We can also express this ratio using fractions:
\[\frac{c}{t} = \frac{5}{9}\]

By cross-multiplying, we get \(5 \times t\) and \(9 \times c\). These values will be equal.

\[9c = 5t\]

We also had \(5t\) in our first equation, so we can substitute \(9c\) in for \(5t\) (since they’re equal).

\[\begin{aligned}7c + 5t &= 480 \\ 16c &= 480 \\ c&=30\end{aligned}\]

Let’s substitute this value into \(5t = 9c\) to find the value of \(t\).

\[\begin{aligned}5t&= 9\times30 \\ &= 270 \\ t&=270\div5 \\&=54\end{aligned}\]

So, 1kg of carrots costs 30p and 1kg of tomatoes costs 54p

Have the mysteries of the Edexcel carrot and tomato question now been revealed? Whatever the answer, we have a great range of helpful blogs here! You can also subscribe to Beyond for access to thousands of secondary teaching resources. You can sign up for a free account here and take a look around at our free resources before you subscribe too.

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