Fredrick had some coupons to sell at a funfair. Each coupon cost $5, On the first day, he sold 264 coupons. On the second day, he sold 1/5 of the remaining coupons. On the third day, he sold the rest of the coupons, and this was 1/3 of the total number of coupons sold on the first two days.
(a) What fraction of the total number of coupons did Fredrick sell on the first day?
(b) Each coupon cost $5. What was the total amount of money Fredrick collected from the sale of coupons over the three days?
(a) Fredrick sold all the coupons he had on the first day, which means he sold all the coupons he had divided by 1. So, the fraction of the total number of coupons sold on the first day is 1.
(b) On the first day, Fredrick sold 264 coupons at $5 each, which gives a total of 264 x $5 = $1320.
On the second day, he sold 1/5 of the remaining coupons. To find out how many coupons he had left, we first need to subtract the 264 coupons he sold on the first day from the total number of coupons he had:
Total number of coupons - coupons sold on first day = remaining coupons
= total number of coupons - 264
We know that Fredrick sold 1/5 of the remaining coupons on the second day, so this means he sold:
1/5 x (total number of coupons - 264) = (total number of coupons - 264)/5 coupons
On the third day, he sold all the remaining coupons, which means he sold:
(total number of coupons - 264) - (total number of coupons - 264)/5 = 4/5 x (total number of coupons - 264) coupons
We also know that the number of coupons he sold on the third day was 1/3 of the total number of coupons sold on the first two days. So we have:
4/5 x (total number of coupons - 264) = 1/3 x (264 + (total number of coupons - 264)/5)
Simplifying this equation, we get:
4/5 x (total number of coupons - 264) = 88 + (total number of coupons - 264)/15
Multiplying both sides by 15, we get:
12 x (total number of coupons - 264) = 1320 + total number of coupons - 264
Expanding and simplifying, we get:
12 x total number of coupons = 16680
So the total number of coupons Fredrick had was:
total number of coupons = 16680/12 = 1390
Therefore, Fredrick sold:
- 264 coupons on the first day
- (1390 - 264)/5 = 225 coupons on the second day
- (1390 - 264) - 225 = 901 coupons on the third day
The total number of coupons sold over the three days is:
264 + 225 + 901 = 1390
And the total amount of money Fredrick collected from the sale of coupons over the three days is:
$5 x 1390 = $6950
(a) To find the fraction of the total number of coupons sold on the first day, we need to divide the number of coupons sold on the first day (264) by the total number of coupons sold over the three days.
Total number of coupons sold = 264 + (1/5) x 264 + (1/3) x (264 + (1/5) x 264)
Total number of coupons sold = 264 + 52.8 + 176.53
Total number of coupons sold = 493.33
Fraction of the total number of coupons sold on the first day = 264/493.33 = 11/16
(b) The total amount of money Fredrick collected from the sale of coupons over the three days can be found by multiplying the number of coupons sold on each day by the cost of each coupon.
Total money collected = (264 x 5) + (52.8 x 5) + (176.53 x 5)
Total money collected = $1920
Alternatively, if we use the total number of coupons sold that we found in part (a), we can directly calculate the total amount of money Fredrick collected:
Total number of coupons sold = 493.33
Total money collected = 493.33 x 5 = $2466.67
(a) To find the fraction of the total number of coupons that Fredrick sold on the first day, we need to calculate the ratio of the number of coupons sold on the first day to the total number of coupons.
Given that Fredrick sold 264 coupons on the first day and the total number of coupons is unknown, we cannot determine the exact fraction. However, we can express it as a fraction by dividing the number of coupons sold on the first day by the total number of coupons:
Fraction = Number of coupons sold on the first day / Total number of coupons.
(b) To calculate the total amount of money Fredrick collected from the sale of coupons over the three days, we need to determine the total number of coupons sold and then multiply it by the cost per coupon.
On the first day, Fredrick sold 264 coupons.
On the second day, Fredrick sold 1/5 of the remaining coupons. If we let x represent the number of remaining coupons after the first day, then on the second day, Fredrick sold (1/5)x coupons.
On the third day, Fredrick sold the remaining coupons, which is (1 - 1/5) or 4/5 of the remaining coupons from the second day. Therefore, on the third day, Fredrick sold (4/5)x coupons.
The total number of coupons sold over the three days is the sum of the coupons sold on each day:
Total number of coupons sold = number of coupons sold on the first day + number of coupons sold on the second day + number of coupons sold on the third day.
Total number of coupons sold = 264 + (1/5)x + (4/5)x.
To determine the total amount of money Fredrick collected, we multiply the total number of coupons sold by the cost per coupon:
Total amount of money collected = Total number of coupons sold × Cost per coupon.
Total amount of money collected = (264 + (1/5)x + (4/5)x) × $5.
To answer these questions, let's break down the information provided.
(a) What fraction of the total number of coupons did Fredrick sell on the first day?
To find the fraction of coupons sold on the first day, we need to compare the number of coupons sold on the first day to the total number of coupons.
The total number of coupons is the sum of the coupons sold on the first day, the second day, and the third day.
Given that Fredrick sold 264 coupons on the first day, we need to calculate the total number of coupons to find the fraction. However, we don't have that information directly.
But we do know that on the second day, he sold 1/5 of the remaining coupons. This means he had (1 - 1/5) or 4/5 of the total coupons remaining after the first day.
On the third day, he sold the rest of the coupons, which was 1/3 of the total number of coupons sold on the first two days. This means the number of coupons sold on the third day is 1/3 of (264 + 1/5 * (4/5 * Total Number of Coupons)).
So, we have the equation: 1/3 * (264 + 1/5 * (4/5 * Total Number of Coupons)) = Total Number of Coupons
Solving this equation will give us the total number of coupons. Once we have that value, we can find the fraction sold on the first day by dividing 264 by the total number of coupons obtained.
(b) Each coupon cost $5. What was the total amount of money Fredrick collected from the sale of coupons over the three days?
To find out the total amount of money collected, we need to multiply the number of coupons sold each day by $5, as each coupon costs $5.
Using the fractions determined from the previous question, we can calculate the money collected on each day and sum them up to find the total amount.