Here is a real-world example working toward the expressions:
Markus is shopping for a deal on a washing machine in a state where there is no sales tax. He finds a model he likes for d dollars; better yet, the model is on sale at 25% off. How can he write expressions showing how much he will pay for the washing machine?
Markus can separate the cost of the washing machine from the amount of the discount by writing two terms. In this case, the first term is d , the cost of the machine. The second term is − 0.25d , the amount of money he will save with his discount. That produces the linear expression d − 0.25d . This is one way Markus can express the total price he will pay.
Markus can also combine the two terms, using 1 − 0.25 is equal to 0.75. Another way to write the expression is 0.75d . Again, one expression keeps the original cost and the discount separate, while the other combines them. The fact that the expressions are equivalent demonstrates that reducing a number by 25% is the same as multiplying it by 0.75.
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In this example, Markus is shopping for a washing machine and wants to find the total price after a 25% discount.
One way to express this is by writing an expression with two terms: d - 0.25d. The first term, d, represents the cost of the machine without any discount. The second term, -0.25d, represents the amount of money Markus will save with the 25% discount.
Another way to express this is by combining the terms. Since 1 - 0.25 equals 0.75, Markus can write the expression as 0.75d. This expression represents the total price after the discount is applied.
It's important to understand the information provided and review the material if anything is unclear.
To summarize, Markus can write two expressions to show how much he will pay for the washing machine:
1. d - 0.25d: This expression separates the cost of the washing machine (d) from the amount of money he will save with his 25% discount (-0.25d).
2. 0.75d: This expression combines the cost of the washing machine with the discount, where multiplying the original cost (d) by 0.75 represents the reduced price.
It's important to comprehend and understand the concepts presented here. If there are any uncertainties, take the time to review the material for better understanding.
To summarize, Markus can write expressions to show how much he will pay for the washing machine in two ways:
1. The expression "d - 0.25d" separates the cost of the machine, represented by 'd', from the discount, which is 25% of the cost.
2. The expression "0.75d" combines the two terms by multiplying the original cost, 'd', by 0.75, which represents a 25% reduction.
It is important to understand the concept that reducing a number by 25% is equivalent to multiplying it by 0.75. Take the time to review and make sure you comprehend the information provided. If you have any doubts, go back and revisit the material.