(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
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?
3 answers
(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
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
Total number of coupons sold = 493.33
Total money collected = 493.33 x 5 = $2466.67