Word problems

To dilute a mixture, the amount of solvent added can be calculated based on the initial and final concentrations of the solute.. If the original volume is 100, there are 30 units of salt.

The sale price after discount is a percentage of the original price.. Since the shirt is discounted by 20%, the sale price of $40 represents 80% of the original price.

To find the original price, we can divide the sale price by the percentage of the original price that the sale price represents, which is 80% or 0.80 in this case. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !People often confuse the percentage of the discount with the percentage of the original price, leading to incorrect calculations.
• !A common mistake is to only consider the speed of one car, or to not account for the fact that the cars are moving towards each other, which would result in an incorrect calculation of the time it takes for them to meet.
• !People often get confused about how to calculate the amount of solvent needed to achieve a specific dilution. A common mistake is not correctly calculating the new total volume required for the desired concentration.
• !Option A is incorrect because it incorrectly calculates the 20% discount based on the sale price of $40 rather than the original price.
• !An answer of 4 hours is incorrect because it fails to account for the second car's speed.

Answer each from memory — you'll see instantly whether you're right and why.

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