Question 1122190: 1.) Fill in the blank with a plausible hourly wage, then solve the problem.
Thomas earns _ per hour, plus tips. At the end of the day, he made exactly $30 less in tips than he did from his hourly wage. In total, he made $131. How much did he make in tips?
2.)There are 100 Grade 9 students at a high school, and 40% of these students went to the football game. The full price for a ticket was $8.00, but half of the Grade 9 students who went to the game wore school colors, so they only had to pay $2.00 for a ticket. What was the total amount of money collected from the Grade 9 students who attended the football game.
3.) Consider the general question (-1)^n is a natural number (1, 2, 3...). What will it evaluate to, for a given value of n?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1.) Fill in the blank with a plausible hourly wage, then solve the problem.
Thomas earns _ per hour, plus tips. At the end of the day, he made exactly $30 less in tips than he did from his hourly wage. In total, he made $131. How much did he make in tips?
it really doesn't matter how much he makes per hour.
he will make the same value in tips at the end of the day.
that value will be 50.5 dollars.
let h = the number of hours he works in a day.
let w = his hourly wages.
let t = the amount of tips he makes in a day.
he makes wh + t in a day.
since he made 131 on a particular day, then wh + t = 131
you are given that he made 30 dollars less in tips than he made from his hourly wage.
this means that t = wh - 30
solve for wh to get wh = t + 30
in the formula of wh + t = 131, replace wh with t + 30 to get t + 30 + t = 131.
combine like terms to get 2t + 30 = 131
solve for t to get t = (131 - 30) / 2 = 50.5 dollars.
2.)There are 100 Grade 9 students at a high school, and 40% of these students went to the football game. The full price for a ticket was $8.00, but half of the Grade 9 students who went to the game wore school colors, so they only had to pay $2.00 for a ticket. What was the total amount of money collected from the Grade 9 students who attended the football game.
40% of 100 grade 9 students = 40 grade 9 students that went to the football game.
half of the grade 9 students wore school colors so they only had to pay 2 dollars for their tickets.
the other half had to pay full fare of 8 collars.
20 * 2 + 20 * 8 = 40 + 160 = 200 dollars that was collected from the grade 9 students that went to the football game.
3.) Consider the general question (-1)^n is a natural number (1, 2, 3...). What will it evaluate to, for a given value of n?
(-1)^n is equal to -1 if n is odd and is equal to 1 if n is even.
as n increases by 1 each time, the function fluctuates between -1 and 1 endlessly.
(-1)^1 = -1
(-1)^2 = 1
(-1)^3 = -1
(-1)^4 = 1
etc.
|
|
|
