Question

1. You have won a contest sponsored by a local radio station. If you are given the

choice of the two payment plans listed below, which plan will pay you more? How

much more?

a. ₱10.00 on the first day, ₱20.00 on the second day, ₱30.00 on the third day,

etc., for two months.


b. ₱10.00 on the first day, ₱20.00 on the second day, ₱40.00 on the third day,

etc. for two weeks.​

Answer 1

Answer:

Plan B will give you ₱145 530.00 more than Plan A.

Step-by-step explanation:

Plan A

G: ₱10.00, ₱20.00, ₱30.00, ...

n=60

a1=₱10.00

d=₱10.00

R:S60

E:Sn=n/2[2a1+)n-1)d]

S:S60=60/2[2(₱10)+(60-1)₱10]

S60=60/2[2(₱10)+59(₱10)]

S60=60/2(₱20+₱590)

S60=60/2(₱610)

S60=₱18 300.00

Plan B

G: ₱10.00, ₱20.00, ₱40.00, ...

n=14

a1=₱10.00

r=2

R:S14

E:Sn=a1(r^n - 1)/r-1

S14=₱10.00(2^14 - 1)/2-1

S14=₱10.00(16 384 - 1)/1

S14=₱10.00(16 383)

S14=₱163 830.00)

Subtract:

₱163 830.00-₱18 300.00=₱145 530.00

P.S: Brainly lang sakalam

Answer 2

Given: You have won a contest sponsored by a local radio station. You are given the choice of the two payment plans listed below:

a. ₱10.00 on the first day, ₱20.00 on the second day, ₱30.00 on the third day etc for two months

b. ₱10.00 on the first day, ₱20.00 on the second day, ₱40.00 on the third day etc for two weeks

To find: Which plan will pay you more and by how much?

Solution: In the first choice, the money increases by ₱10.00 daily. This sequence forms an arithmetic progression (AP) where first term is ₱10.00 and common difference (daily increase in money) is ₱10.00.

Number of days

= 2 months × 30 days( 1 month = 30 days)

= 60 days

Let the first term be a, common difference be d and number of days be n.

Total amount will be equal to sum of AP which is calculated by the formula:

$\frac{n}{2} (2a + (n - 1)d)$

$= \frac{60}{2} (2 \times 10 + (60 - 1) \times 10)$

$= 30(20 + 590)$

= 30 × 610

= 18,300

In the second choice, the money increase by 2 times the previous day. This sequence forms a geometric progression (GP) where first term is ₱10.00 and common ratio, that is, number of times by which the money increases from previous day, is 2.

Number of days

= 2 weeks × 7 days

= 14 days

Let the first term be a, common ratio be r and number of terms(days) be n.

Total amount will be sum of GP which is given by the formula:

$a \frac{ {r}^{n} - 1 }{r - 1}$

$= 10 \frac{ {2}^{14} - 1}{2 - 1}$

$= 10(16384 - 1)$

= 10 × 16383

= 1,63,830

Clearly, the second choice where the money increases in GP is a better option.

Difference in money

= ₱1,63,830- ₱18,300

= ₱1,45,530

The second plan will pay more. It pays ₱1,45,530 more than the first plan.