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dexar [7]
3 years ago
10

Sally's cat is 3 years older than Helen's dog. The product of their ages is 54. How old is Helen's dog?

Mathematics
1 answer:
viva [34]3 years ago
7 0
The first thing that we have to do is to assign variables to the cat's and the dog's ages. Let us use c to represent the age of the cat and d for the dog's age. So, let's translate the word problem into a mathematical one.

c = d + 3

This is the first equation while the second equation is

(d+3)*d = 54

which becomes 

d^2 +3d -54 = 0

which can be factored into (d-6)(d+9). This gives us two roots which are 6 and -9. However, age is a non-negative number so we will take 6 as the age of Helen's dog. Thus, making Sally's cat 9 years old.
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Mr. Smith traveled to a city 300 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 6
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Answer: The speed at which he traveled to the city is 69.8 mph

Step-by-step explanation:

Let x represent the speed at which he traveled to the city.

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Time taken to travel to the city is

300/x

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300(x - 6) + 300x = 9x(x - 6)

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9x² - 54x - 300x - 300x - 1800 = 0

9x² - 654x -1800 = 0

Applying the general quadratic equation,

x = [- b ± √(b² - 4ac)]/2a

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x = [- - 654 ± √(- 654² - 4 × 9 × 1800)]/2 × 9

x = [654 ± √(427716 - 64800)]/18

x = [654 ± √362916.4]/18

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By checking,

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4.3 + 4.7 = 9 hours

3 0
3 years ago
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