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187 kg of carrots and 5 kg of tomatoes cost a total of 480 pence.

The cost ratio of 1 kg of carrots to 1 kg of tomatoes is [tex]5:9[/tex].

Work out the cost of 1 kg of carrots and the cost of 1 kg of tomatoes.

Answer :

Let the cost per kilogram of carrots be [tex]$5x$[/tex] and the cost per kilogram of tomatoes be [tex]$9x$[/tex], since the ratio is given as [tex]$5:9$[/tex].

We are told that [tex]$187$[/tex] kg of carrots and [tex]$5$[/tex] kg of tomatoes cost a total of [tex]$480$[/tex] p. This gives the equation

[tex]$$
187(5x) + 5(9x) = 480.
$$[/tex]

Simplify the terms:

[tex]$$
935x + 45x = 980x = 480.
$$[/tex]

Solve for [tex]$x$[/tex]:

[tex]$$
x = \frac{480}{980} = \frac{24}{49} \approx 0.4898.
$$[/tex]

Now, substitute [tex]$x$[/tex] back into the expressions for the cost per kilogram:

1. For carrots:

[tex]$$
\text{Cost per kg of carrots} = 5x = 5 \times \frac{24}{49} = \frac{120}{49} \approx 2.449 \text{ p}.
$$[/tex]

2. For tomatoes:

[tex]$$
\text{Cost per kg of tomatoes} = 9x = 9 \times \frac{24}{49} = \frac{216}{49} \approx 4.408 \text{ p}.
$$[/tex]

Thus, the cost of [tex]$1$[/tex] kg of carrots is approximately [tex]$2.449$[/tex] p and the cost of [tex]$1$[/tex] kg of tomatoes is approximately [tex]$4.408$[/tex] p.

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