1. A music store pays €14 for a CD. At what price must the CD be sold so the shopkeeper can make a profit of 25%?
2. What is the smallest number which can be divided evenly by 500, 600, 1000?
3. A map scale is 1cm to 30km. What is the real distance between two towns which are 1.5cm apart on the map?
4. The average age of four women is 25. If the average age of three of them is 24, what is the age of the other woman?
1) cost is Euro14 per CD
shopkeeper wants 25% profit
that means he/she wants to sell each CD for 25% more than the cost
how do you increase 14 so that it's 25% more than 14?
maybe multiply 14 by (1 + 25%) = 14 * 1.25 ??
4)
(W1 + W2 + W3 +W4)/4 = 25
(Wx + Wy + Wz)/3 = 24
so (W1 + W2 + W3 +W4) = 100
and (Wx + Wy + Wz) = 72
what's missing from the second sum?
1. To find the selling price of the CD, we need to calculate a 25% profit on the cost price.
First, determine the profit amount by multiplying the cost price (€14) by the profit percentage (25%) in decimal form:
Profit = €14 * 0.25 = €3.50
Then, add the profit to the cost price to get the selling price:
Selling price = Cost price + Profit = €14 + €3.50 = €17.50
Therefore, the CD must be sold at a price of €17.50 in order for the shopkeeper to make a profit of 25%.
2. To find the smallest number that can be divided evenly by 500, 600, and 1000, we need to find their least common multiple (LCM).
The LCM is the smallest multiple that is divisible by all the given numbers.
To find the LCM, we can use the prime factorization method:
Prime factorization of 500: 2^2 * 5^3
Prime factorization of 600: 2^3 * 3 * 5^2
Prime factorization of 1000: 2^3 * 5^3
Take the highest power of each prime factor that appears in any of the numbers:
2^3 * 3 * 5^3 = 1000
Therefore, the smallest number that can be divided evenly by 500, 600, and 1000 is 1000.
3. The map scale is given as 1cm to 30km, meaning that 1cm on the map represents a distance of 30 kilometers in reality.
If the distance between two towns on the map is 1.5cm, we can find the real distance between the towns by multiplying the map distance by the scale factor:
Real distance = Map distance * Scale factor
Real distance = 1.5cm * 30km/cm = 45km
Therefore, the real distance between the two towns is 45 kilometers.
4. The average age of four women is 25, and the average age of three of them is 24.
To find the age of the other woman, we need to find the total age of the four women and subtract the sum of the ages of the three women.
The sum of the ages of the four women is 25 * 4 = 100.
The sum of the ages of the three women is 24 * 3 = 72.
Therefore, the age of the other woman is the difference between the total age and the sum of the ages of the three women:
Age of the other woman = Total age - Sum of ages of three women
Age of the other woman = 100 - 72 = 28 years.
Therefore, the age of the other woman is 28 years.