1) A certain radio costs a merchant $72, which includes overhead and selling expenses. At what price must he sell it if he is to make a profit of 20% on the selling price?
a) $86.40 b) $90 c) $92 d)$144
e)none of these answers
2) Daniel gave 4/5 of his stickers to Javier. Javier's collection of stickers increased to 64. If Javier had 28 stickers in the beginning, how many stickers did Daniel have in the beginning?
Please help and thank you in advance.
profit = .2 S
cost = 72
72 + .2 s = s
72 = .8 s
s = 90
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Javier had J = 28
28 + (4/5) D = 64
(4/5) D = 36
D = 45
1) To solve this question, we need to calculate the selling price that includes a 20% profit on the selling price. Let's break it down step by step:
First, we need to find the cost price of the radio before any profit is added. We know that the cost, including overhead and selling expenses, is $72.
Let's denote the selling price as 'x'.
To calculate the cost price, we set up the following equation:
x - 20% of x = $72
Simplifying this equation, we get:
x - 0.2x = $72
0.8x = $72
Dividing both sides by 0.8, we find:
x = $90
Therefore, the selling price that includes a 20% profit on the selling price is $90.
So, the correct answer in this case is option b) $90.
2) To solve this question, we can set up the following equation based on the given information:
(4/5) * Daniel's stickers = 64 - 28
Let's solve this equation step by step:
First, we need to find the number of stickers that Daniel originally had. Let's denote this value by 'x'.
So, the equation becomes:
(4/5) * x = 64 - 28
Simplifying this equation, we get:
4x/5 = 36
To isolate 'x', we can multiply both sides of the equation by 5/4:
(4/5) * 5/4 * x = 36 * 5/4
Simplifying further, we find:
x = 45
Therefore, Daniel originally had 45 stickers.
I hope this helps! Let me know if you have any further questions.
1) Let's assume the selling price of the radio is "x" dollars.
Given that the merchant wants to make a profit of 20% on the selling price, the profit made on selling the radio would be 20% of x, which is 0.2x.
So, the total amount the merchant wants to sell the radio for is the cost price (including overhead and selling expenses) plus the profit. We can set up the equation:
x = 72 + 0.2x
Solving this equation for x:
0.8x = 72
x = 72 / 0.8
x = 90
Therefore, the merchant must sell the radio for $90.
So, the answer is b) $90.
2) Let's assume that Daniel initially had "x" stickers.
Given that Daniel gave 4/5 of his stickers to Javier, he retained 1/5th of his original stickers, which is (1/5)x.
Javier's collection of stickers increased to 64, meaning he received the remaining 4/5th of Daniel's original stickers, which is (4/5)x.
We are given that (4/5)x = 64.
Solving this equation for x:
x = 64 * (5/4)
x = 80
Therefore, Daniel had 80 stickers in the beginning.
So, the answer is 80 stickers.