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(a)A company made

4
go-kart engines using
39.2
kilograms (
kg
) of molten steel. Cooling the engines after the manufacturing process required
8
liters of water for each kilogram of steel. The company would like to make
6
go-kart engines using the same amount of steel in each engine as last time.
Fill in the blanks below. Then use the diagram to show the steel and water needed to make
6
go-kart engines.

Amount of steel used for each engine:
kg
Amount of water used for each engine:
liters
1 engine
kg
liters
1 engine
kg
liters
2 engines
(b)How much water is needed to make
6
go-kart engines?
liters

1 answer

To solve the problem, we need to determine the amount of steel used for each engine, and then calculate the amount of water needed.

(a)

  1. Calculate the amount of steel used for each go-kart engine: \[ \text{Total steel} = 39.2 \text{ kg} \] \[ \text{Number of engines} = 4 \] \[ \text{Steel per engine} = \frac{\text{Total steel}}{\text{Number of engines}} = \frac{39.2 \text{ kg}}{4} = 9.8 \text{ kg/engine} \]

    Therefore, the amount of steel used for each engine is \(9.8 \text{ kg}\).

  2. Calculate the amount of water used for each engine: \[ \text{Water per kg of steel} = 8 \text{ liters} \] \[ \text{Water for each engine} = \text{Steel per engine} \times \text{Water per kg of steel} = 9.8 \text{ kg/engine} \times 8 \text{ liters/kg} = 78.4 \text{ liters/engine} \]

    Therefore, the amount of water used for each engine is \(78.4 \text{ liters}\).

Now we can fill in the blanks:

  • Amount of steel used for each engine: 9.8 kg
  • Amount of water used for each engine: 78.4 liters

Using the diagram to show the steel and water needed for each number of engines:

  • 1 engine:

    • Steel: 9.8 kg
    • Water: 78.4 liters

  • 2 engines:

    • Steel: \(9.8 \text{ kg} \times 2 = 19.6 \text{ kg}\)
    • Water: \(78.4 \text{ liters} \times 2 = 156.8 \text{ liters}\)

(b) How much water is needed to make 6 go-kart engines?

  1. Calculate the total water needed for 6 engines: \[ \text{Water for 6 engines} = \text{Water per engine} \times 6 = 78.4 \text{ liters} \times 6 = 470.4 \text{ liters} \]

So, the amount of water needed to make 6 go-kart engines is \(470.4\) liters.