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Weight and Cost Conversions

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Weight and Cost Conversions

Show your working. Give money answers in dollars and cents unless the question asks for a different form.

Weight and cost problems

1.A spice shop charges $96 per kilogram for a seasoning. A baker needs 220 g, but the shop sells it only in 40 g portions. What is the smallest amount the baker must buy, how much will it cost, and how many grams will be left over?

2.A rare ingredient costs $6,400 per kilogram. Find its price per milligram. Then calculate the cost of 0.625 g and express that cost in scientific notation.

3.A food supplier charges $92 for 2/5 kg of a specialty ingredient. The price per kilogram then rises by 10%. What will 1.8 kg cost at the increased rate?

4.A baking mix contains flour, sugar and butter in the ratio 4:3:1. The whole mix weighs 3.2 kg. Flour costs $2.75/kg, sugar costs $4.20/kg and butter costs $9.50/kg. Work out the cost of all the ingredients.

5.A retailer buys 12.4 kg of grain at $21.50 per kilogram and receives a 10% discount on the purchase. After using 7.6 kg, the retailer sells all the remaining grain at 25% above the original price per kilogram. Compared with the discounted purchase cost, what is the retailer’s profit or loss?

6.Three laboratories order a compound priced at $3,200 per kilogram. Lab A needs 0.45 kg. Lab B needs 2/3 of Lab A’s amount, and Lab C needs 125% of Lab B’s amount. Their combined order receives a 6% discount, shared between the labs in proportion to the weight each ordered. How much does each lab pay?

7.An investor buys 0.0625 kg of a metal when its price is $72,000 per kilogram. The price then rises by 10%, falls by 6%, and rises by 7%, in that order. What is the investment worth after all three changes? Round to the nearest cent.

8.A bakery makes 12.5 kg of flour blend using 50% bread flour at $3.20/kg, 30% cake flour at $4.40/kg and 20% specialty flour at $8.50/kg. Find the mass of each flour in grams and the total cost of the blend.

9.A café buys 7.5 kg of beans at $52.40 per kilogram. It uses 2/3 of the beans. Of what remains, 8% is defective and cannot be sold. The café sells the good remaining beans for $68 per kilogram. Compared with the original purchase cost, what is the café’s profit or loss?

10.A supplier charges $78,000 per kilogram for a catalyst. For each shipment, orders of up to 500 g receive no discount, orders from 501 g to 1 kg receive 5% off, and orders over 1 kg receive 12% off the whole shipment. A research centre needs 1.35 kg. Is one shipment or two shipments of 0.50 kg and 0.85 kg cheaper? Calculate the cheaper total and its savings compared with buying all 1.35 kg at the undiscounted rate.