Dana needs 300 pickets for her colorful picket fence. She wants equal amounts of each of her 4
selected colors. She already has 32 red, 26 green, 9 yellow and no blue. How many more of each
color does Dana need to buy? If the bulbs cost 25 cents and you get 20% off if you purchase 50 or
more of the same color and 30% off if you purchase 60 or more of one color, how much does Dana
need to spend?
Well, it seems like Dana has quite the pickety situation on her hands! Let's break it down.
Currently, Dana already has 32 red pickets, but she needs 75 (300 divided by 4) in total. So, she needs to buy an extra 43 red pickets.
For green, she has 26 but needs 75, so she needs to buy an extra 49 green pickets.
As for yellow, she has 9 and needs 75, so she needs to buy an extra 66 yellow pickets.
Lastly, she needs 75 blue pickets, and since she has none right now, she needs to buy 75 blue pickets.
In summary, Dana needs to buy:
- 43 red pickets
- 49 green pickets
- 66 yellow pickets
- 75 blue pickets
Now, let's crunch some numbers for the cost. We know that each picket costs 25 cents, but Dana can also get a discount if she buys certain amounts.
For the red pickets, if she buys 50 or more, she gets a 20% discount. So, let's calculate:
43 red pickets at 25 cents each = $10.75
Since she bought more than 50 red pickets, let's apply the 20% discount:
$10.75 - 20% = $8.60
For the green and yellow pickets, she doesn't qualify for any discounts since she wants less than 50 of each color. So, let's calculate:
49 green pickets at 25 cents each = $12.25
66 yellow pickets at 25 cents each = $16.50
As for the blue pickets, she's also not eligible for any discounts. So:
75 blue pickets at 25 cents each = $18.75
Now, let's add up all the costs:
$8.60 (red pickets) + $12.25 (green pickets) + $16.50 (yellow pickets) + $18.75 (blue pickets) = $56.10
So, Dana needs to spend a total of $56.10 to get all the needed pickets for her colorful picket fence. I hope she's not feeling too pickety about it!
To find out how many more of each color Dana needs to buy, we need to determine the total number of pickets she already has and then subtract it from the desired total.
First, we find the total number of pickets she already has:
Total pickets Dana already has = Number of red pickets + Number of green pickets + Number of yellow pickets + Number of blue pickets
Total pickets Dana already has = 32 + 26 + 9 + 0 = 67 pickets
Next, we calculate the total number of pickets needed for each color:
Total number of pickets needed for each color = Total number of pickets needed / Number of colors
Total number of pickets needed for each color = 300 / 4 = 75 pickets per color
Now, we find the number of pickets Dana needs to buy for each color:
Number of red pickets Dana needs to buy = Total number of pickets needed for each color - Number of red pickets she already has
Number of red pickets Dana needs to buy = 75 - 32 = 43 pickets
Number of green pickets Dana needs to buy = Total number of pickets needed for each color - Number of green pickets she already has
Number of green pickets Dana needs to buy = 75 - 26 = 49 pickets
Number of yellow pickets Dana needs to buy = Total number of pickets needed for each color - Number of yellow pickets she already has
Number of yellow pickets Dana needs to buy = 75 - 9 = 66 pickets
Number of blue pickets Dana needs to buy = Total number of pickets needed for each color - Number of blue pickets she already has
Number of blue pickets Dana needs to buy = 75 - 0 = 75 pickets
Now, let's calculate the cost of the pickets Dana needs to buy, taking into account the discounts:
The cost per picket is 25 cents.
For the red pickets:
If Dana purchases 50 or more of the same color, she will receive a 20% discount.
Total cost of red pickets = Number of red pickets Dana needs to buy * Cost per picket * (1 - Discount)
Total cost of red pickets = 43 * $0.25 * (1 - 0.20) = $8.15
For the green pickets:
If Dana purchases 50 or more of the same color, she will receive a 20% discount.
Total cost of green pickets = Number of green pickets Dana needs to buy * Cost per picket * (1 - Discount)
Total cost of green pickets = 49 * $0.25 * (1 - 0.20) = $9.29
For the yellow pickets:
If Dana purchases 60 or more of the same color, she will receive a 30% discount.
Total cost of yellow pickets = Number of yellow pickets Dana needs to buy * Cost per picket * (1 - Discount)
Total cost of yellow pickets = 66 * $0.25 * (1 - 0.30) = $11.55
For the blue pickets:
If Dana purchases 60 or more of the same color, she will receive a 30% discount.
Total cost of blue pickets = Number of blue pickets Dana needs to buy * Cost per picket * (1 - Discount)
Total cost of blue pickets = 75 * $0.25 * (1 - 0.30) = $13.12
Finally, we calculate the total cost Dana needs to spend:
Total cost = Total cost of red pickets + Total cost of green pickets + Total cost of yellow pickets + Total cost of blue pickets
Total cost = $8.15 + $9.29 + $11.55 + $13.12 = $42.11
Therefore, Dana needs to buy 43 more red pickets, 49 more green pickets, 66 more yellow pickets, and 75 more blue pickets, and she needs to spend a total of $42.11 on the pickets.
Guys the answer is 46.68 it's actually 10.75 + 12.25+ 11.55+ 13.13
Which equals to 46.68
The correct answer to this question is $53.30. Being that she needs equal amounts, she needs 75 of each color.
She already has 32 red, so that leaves 43 more that she needs : costs 4325=$10.75
She already has 26 green, so that leaves 49 more that she needs. : costs 4925=$12.25
She already has 9 yellows, so she needs 66 more of those. 6625=$16.50. She only pays 70% of this because 30% gets knocked off. 70% of $16.50 = $11.55
She has no blues yet, so she needs all 75 of those. It would originally cost 7525=$18.75. She only pays 70% of this. 70% of $18.75 = $13.13
Adding together all of the amounts, leads to 10.75 + 12.25 + 11.55 + 18.75, which equals $53.30