Answer to Question #151584 in Algebra for Miya

Question

John is saving money for his summer vacation. He starts on the 1st day by placing one dollar in his special summer savings box. Each day he saves 25 cents more than the day before. Provide a complete, accurate and appropriately labeled graph and accompanying table in your solution.
a) How much will he deposit into the savings box on the 10th day?
b) When he begins his summer vacation, he has saved for 47 days.
How much will he have saved in all?

Answer 1

Let`s start solving by by defining given values:

a₁=1 this is the first day of his saving money and he increased amount of daily saving money

d=a₁+0.25=1.25 this continious until he stopped.

a) We need to find how much he saved in the 10th day:

a₁₀=a₁+$(n-1)\times d$, n is number f days, So:

a₁₀=1+$9\times 0.25$ = 3.25 dollors, he put 3.25 dollors in 10th day of his charity

b) In this case, n equal to 47:

a₄₇=a₁+$(n-1)\times d$=1+46$\times$ 0.25=12.5 dollors

S(sum of saved money)=(a₁+a₄₇) $\times \frac{47}{2}$ = (1+12.5) $\times \frac{47}{2}$=317.25 dollors he saved in total.