Anthony earns an allowance for doing work at home .the first day he earns $1. ,$2. for the next two days,$3.for the next three days and so on and so on.If Anthony keep earning money this way ,on what day will he earn $6.?(2)Anthony saves all the money he earn to buy a $59.99 videa game.How much money wiil he save on the first day his mom pays him $6.for doing chores?will ANthony have enough money to buy the video game?Explain.
Anthony earns an allowance for doing work at home .the first day he earns $1. ,$2. for the next two days,$3.for the next three days and so on and so on.If Anthony keep earning money this way ,on what day will he earn $6.?(2)Anthony saves all the money he earn to buy a $59.99 videa game.How much money wiil he save on the first day his mom pays him $6.for doing chores?will ANthony have enough money to buy the video game?Explain.
To find out on which day Anthony will earn $6, we need to determine the pattern of his earnings. From the information given, we see that on the first day, he earns $1, on the next two days he earns $2 each day, and on the following three days, he earns $3 each day.
So, the pattern is that Anthony's earnings increase by $1 each day. We can represent this pattern using the arithmetic sequence formula: an = a + (n-1)d, where "a" is the first term, "n" is the number of the term, and "d" is the common difference.
In this case, "a" is $1 and "d" is $1. Let's plug in the values and solve for "n" when the earnings equal $6:
6 = 1 + (n-1) * 1
5 = n-1
n = 6
Therefore, Anthony will earn $6 on the 6th day.
Moving on to the second question, let's determine how much money Anthony will save on the first day his mom pays him $6 for doing chores. From the given information, we know that Anthony saves all the money he earns.
When his mom pays him $6, this will be the total amount he earns for that day. Therefore, he will save the entire $6.
Finally, let's check if Anthony will have enough money to buy the $59.99 video game. We know that he saves all the money he earns, and to buy the game, he needs $59.99.
Since Anthony only earns $6 per day, we can calculate the number of days he needs to reach $59.99 by dividing the total amount needed by the amount he saves each day:
59.99 / 6 ≈ 10
Therefore, Anthony needs around 10 days to save enough money to buy the video game.