What is the reason for each step in the solution of the equation?
1 answer:
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9514 1404 393
Answer:
k = 5
Step-by-step explanation:
Suppose the distance to the factory is 1 unit. Then the speed the father walks is ...
speed = distance/time = 1 / 30 . . . . units per minute
When the father leaves 10 minutes earlier than the son, his position t minutes after the son starts walking is ...
d = 1/30(t +10)
Similarly, when the father starts 5 minutes earlier than the son, his position t minutes after the son starts walking is ...
d = (1/30)(t +5)
We want that to be the same as the distance the son covers t minutes after he starts walking. The son's progress is ...
d = 1/20t
To find the value of k such that the distance covered is the same 2k minutes after the son starts, we will use t=2k and d=d, so ...
(1/30)(2k +5) = (1/20)(2k)
4k +10 = 6k . . . . . multiply by 60
10 = 2k . . . . . . . . . subtract 4k
5 = k . . . . . . . . . . . divide by 2
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The attached graph shows the different scenarios, where the blue line is the son's progress. When the father starts 5 minutes earlier, the son meets him half-way to the factory after 10 minutes, so k = 10/2 = 5.
Answer:
The expressions for each statement are as follows:
a: 2500+(0.10*2500)
b: 40 * 0.85
c: 250 + (0.075*250)
Step-by-step explanation:
<u>Part a:</u>
Given
Salary = $2500
Percentage of raise = 10%
The new salary will be:
<u>Part b:</u>
Given
Total questions = 40
Percentage of correct answers = 85%
The required expression for correct answers is:
<u>Part c:</u>
Given
Price of phone = $250
Percentage of sales tax = 7.5%
The required expression is:
Hence,
The expressions for each statement are as follows:
a: 2500+(0.10*2500)
b: 40 * 0.85
c: 250 + (0.075*250)