Why is Write an Equation a good strategy for solving this problem?

1. What is the formula for compound interest?

Rus_ich [418]

Answer:

1. CI = P (1 + $\frac{r}{100}$ )^ n - P

CI = A - P

Where P is Principal

R is interest rate

n is number of years

2. a. Semi annually - four times in a year

b. Monthly - two times in a year

c. annually - once in a year

Step-by-step explanation:

1. Money is said to be lent at compound interest , when the interest has become due at certain fixed period say, one year, half year, etc.., is given not paid to money lender, but is added to sum lent . The amount thus obtained become principal for next month and this process repeat until last period .

i.e CI = Final period - Initial period

or CI = A - P

or CI = P(1+ $\frac{r}{100}$ ) ^n - P

2. (a) Semi annually

A = P (1 + $\frac{r}{4 * 100}$ )^ n × 4

(b) Monthly

A = P (1 + $\frac{r}{2 * 100}$ ) ^ n × 2

(c) Annually

A = P (1 + $\frac{r}{100}$ ) ^ n

3 0

3 years ago

A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the rati

AnnyKZ [126]

Answer:

3:7

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%.