Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 2 • Question 19

Ragner plants seeds in three different pots: pot A, pot B, and pot C. He plants a total of 50 seeds. The number of seeds he plants in pot A is equal to the number of seeds he plants in pot B. The number of seeds that he plants in pot C is half the number that he plants in pot B. Work out the number of seeds that he plants in each pot.

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Video Transcript

Ragner plants seeds in three different pots: pot A, pot B, and pot C. He plants a total of 50 seeds. The number of seeds he plants in pot A is equal to the number of seeds he plants in pot B. The number of seeds that he plants in pot C is half the number that he plants in pot B. Work out the number of seeds that he plants in each pot.

We’re told that Ragner plants seeds in three different pots, pot A, pot B, and pot C. He plants a total of 50 seeds. Therefore, the number of seeds in pot A plus the number of seeds in pot B plus the number of seeds in pot C must equal 50. We’re also told that the number of seeds he plants in pot A is equal to the number of seeds he plants in pot B. Finally, we’re told that the number of seeds in pot C is half the number of seeds in pot B.

We can begin by letting the letter 𝑥 be the number of seeds that Ragner plants in pot A. The number of seeds in pot A is the same as the number of seeds in pot B. This means that there will also be 𝑥 seeds in pot B. As there are half as many seeds in pot C as pot B, the number of seeds in pot C will be equal to a half of 𝑥. We can use this information to form the following equation. 𝑥 plus 𝑥 plus a half 𝑥 is equal to 50.

One way of solving this equation would be to firstly group or collect the like terms, in this case group the three 𝑥 terms. 𝑥 is the same as one 𝑥. Therefore, we have one 𝑥 plus one 𝑥 plus a half 𝑥. One plus one plus a half is equal to two and a half. And we know that two and a half is the same as 2.5. On the left-hand side, the 𝑥 terms group to give us 2.5𝑥. This is equal to 50. We can then divide both sides of the equation by 2.5. 2.5 divided by 2.5 is equal to one. Therefore, 2.5𝑥 divided by 2.5 gives us 𝑥. On the right-hand side, 50 divided by 2.5 is equal to 20. There are two 2.5s in five. Therefore, there must be 20 of them in 50.

The solution to the equation is 𝑥 equals 20. This means that the number of seeds in pot A is 20. As pot B had the same number of seeds as pot A, then pot B must also have 20 seeds. Pot C had half the number of seeds as pot B. A half of 20 is equal to 10. Therefore, pot C has 10 seeds. 20 plus 20 plus 10 is equal to 50. This means that our answer is correct.

Ragner plants 20 seeds in pot A, 20 seeds in pot B, and 10 seeds in pot C.

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