# The Edexcel 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.

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.