kim buys pet food in 1.5kg packs, het pet needs 0.8kg of food each week. She wants to have enough food for the next 14 weeks. She already has two 1.5kg packs. Work out the smallest number of packs she needs to buy.

Explanation:

"She already has two 1.5kg packs" means she already has 2*1.5 = 3 kg of food.

The statements "her pet needs 0.8 kg of food each week" and "She wants to have enough food for the next 14 weeks" tell us that she needs 0.8*14 = 11.2 kg of food total.

Let,

x = number of packs she needs to buy

1 pack = 1.5 kg of food

x packs = 1.5x kg of food

Add on the 3 kg of food she already has to get 1.5x+3

The expression 1.5x+3 represents how much food she'll have total after buying x packs.

Set this equal to 11.2 and solve for x

1.5x+3 = 11.2

1.5x+3-3 = 11.2-3 ... subtracting 3 from both sides

1.5x = 8.2

1.5x/(1.5) = 8.2/(1.5) dividing both sides by 1.5

x = 5.4667 approximately

x = 6 rounding up to the nearest whole number

We round up instead of down.

This is because if x = 5, then,

1.5*x+3 = 1.5*5+3 = 7.5+3 = 10.5, but this is less than 11.2

However, if x = 6, then,

1.5*x+3 = 1.5*6+3 = 9+3 = 12 which clears the hurdle of 11.2

So this means buying 6 packages of food is the smallest amount needed to ensure her pet has enough food for the next 14 weeks.

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