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Harrizon [31]
3 years ago
6

Problem 2 : Using in the pattern in the image below, how many dots would be in Step 4

Mathematics
1 answer:
zimovet [89]3 years ago
7 0

Answer:

20

Step-by-step explanation:

One pattern is that we are adding one row and one column for each step.

The first step has 1 row and 2 columns,

the second one has 2 rows and 3 columns,

and the third has 3 rows and 4 columns.

Thus, it would make sense for the fourth step to have 4 rows and 5 columns. This makes a rectangle with a length and a width, with the area of the rectangle being length * width. 4 * 5 = 20 as our number of dots

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Reverse the two digits of my age, divide by three, add 20, and the result is my age. How many years old am I
lapo4ka [179]

Answer:

  • 48 years old.

Step-by-step explanation:

Let the age be xy or 10x + y.

Reverse the two digits of my age, divide by three, add 20, and the result is my age, convert this to equation:

  • (10y + x)/3 + 20 = 10x + y
  • (10y + x)/3 = 10x + y - 20
  • 10y + x = 3(10x + y - 20)
  • 10y + x = 30x + 3y - 60
  • 30x - x + 3y - 10y = 60
  • 29x - 7y = 60

We should consider both x and y are between 1 and 9 since both the age and its reverse are 2-digit numbers.

Possible options for x are:

  • 29x ≥ 7*1 + 60 = 67 ⇒ x > 2, at minimum value of y,

and

  • 29x ≤ 7*9 + 60 = 123 ⇒ x < 5, at maximum value of y.

So x can be 3 or 4.

<h3>If x = 3</h3>

  • 29*3 - 7y = 60
  • 87 - 7y = 60
  • 7y = 27
  • y = 27/7, discarded as fraction.

<h3>If x = 4</h3>

  • 29*4 - 7y = 60
  • 116 - 7y = 60
  • 7y = 56
  • y = 8

So the age is 48.

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