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Ilya [14]
3 years ago
7

Amy wants to buy a new set of paints. At store A, the cost is $22.00, and she has a coupon for 20% off. At store B, the cost is

$22.50, and she has a coupon for $5 off. Which store has the better buy, and why?
Mathematics
1 answer:
Afina-wow [57]3 years ago
8 0

Answer:

Store B

Step-by-step explanation:

Store A

20% is just 1/5 in percent form

22.00= 22*1/5 = 22/5 = 4.40

22.00-4.40=17.6

Store B

22.50-5=17.5

Now you can see that 17.5 is less than 17.6 by 0.1

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Answer:

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Step-by-step explanation:

So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or <em>20%</em> is alcohol. So let's just say that x=alcohol and y=water, this means that: x+y=c  where c is the total amount in the glass. This means that: x=0.20c

Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: j+k=c and that: j=0.40c.

So if we're going to add the two glasses, we simply add the two sides, and get: j+x+k+y=2c. Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: (0.4c+0.2c)+x+k=2c Now we can add like terms to get the equation: 0.6c+y+k=2c. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.

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