The document contains 3 math word problems involving the distribution of money and items in pyramid formations. The first problem distributes $1,000,000 among 5 people with each subsequent person receiving $50,000 less. It is determined that each person receives $300,000, $250,000, $200,000, $150,000, and $100,000 respectively. The second problem involves placing boxes of detergent in a pyramid formation with 15 boxes on the bottom row, calculating there would be a total of 120 boxes. The third problem has a pyramid of blocks with 26 blocks on the bottom row and 2 fewer blocks per subsequent row, calculating there are a total of 182 blocks.

1. Ms. G. Martin

2. Problem Solving
1. The amount of Php 1,000,000.00 is distributed
among five people so that each person after the first
receives Php 50,000.00 less than the preceding person.
How much does each child receive?

3. Identify the given information:
Sn = Php 1,000,000.00(amount to be
distributed)
n= 5 (number of child)
d = -50,000.00
Solution:
Using the formula:
Sn =
𝑛
2
[ 2A1 + (n – 1)d ]
1,000,000 =
5
2
[ 2A1 + (5 – 1)-50,000]
2,000,000 = 5[ 2A1 + (4)-50,000 ]
2,000,000 = 5[2A1 – 200,000]
2,000,000 = 10A1 – 1,000,000
2,000,000 + 1,000,000 = 10A1
3,000,000 = 10A1
3,000,000
10
= A1
300,000 = A1
A1 = 300,000
A2 = A1 – 50,000 = 250,000
A3 = A2 -50,000 = 200, 000
A4 = A3 – 50,000 = 150,000
A5 = A4 – 50,000 = 100,000
Therefore, each child receives the amount
in the sequence of Php300,000,
Php250,000, Php200,000, Php150,000,
Php100,000

4. Problem Solving
2. In a display window, a store owner planned to place
boxes of detergent in pyramid form so that the bottom
row contains 15 b0xes, and so on, with one box on top.
How many boxes of detergent are necessary for the
pyramid?

5. Identify the given information.
An = 15 boxes (last term)
A1 = 1 (first box of 1st element)
d = 1 (common difference)
n= (15 number of rows)
Sn = ?
Solution:
Using the formula:
Sn =
𝒏
𝟐
[ 2A1 + (n – 1)d ]
Sn =
15
2
[ 2(1) + (15 – 1)1 ]
Sn =
15
2
[ 2 + (14)1 ]
Sn =
15
2
[2 + 14]
Sn =
15
2
[16]
Sn = 120
Or using the formula
Sn =
𝒏
𝟐
( A1 + An)
Sn =
15
2
( 1 + 15)
Sn =
15
2
(16)
Sn = 120
The number of boxes of detergent are needed
for the pyramid is 120.

6. Problem Solving
3. A pyramid of blocks has 26 blocks in the bottom row
and 2 fewer blocks in each successive row thereafter.
How many blocks are there in the pyramid?

7. Identify the given information:
d = 2 (common difference)
An= 26
n = 13 = (
26
2
) = since there are 2
fewer blocks in each successive row
thereafter.
A1 = 2
Solution:
Using the formula:
Sn =
𝒏
𝟐
[ 2A1 + (n – 1)d ]
Sn =
13
2
[ 2(2) + (13 – 1)2 ]
Sn =
13
2
[ 4 + (12)2 ]
Sn =
13
2
[ 4 + (24 ]
Sn =
13
2
[ 28 ]
Sn = 182
Or use the formula Sn =
𝑛
2
( A1 + An)
Sn =
13
2
( 2 + 26)
Sn =
13
2
[ 28 ] = Sn = 182
There are 182 blocks in the
pyramid.