A collection of coins contains only 10-cent and 5-cent coins.There are x 5cent coins in the collection. Write an algebraic expression for of following.
* The total value of the coins if for every three 10-cent coins there are five 5-cent coins.
Alright, let's have some fun with this one!
To find the total value of the coins, we need to consider the number of 10-cent coins and the number of 5-cent coins.
Let's start by determining the number of 10-cent coins. The problem states that for every three 10-cent coins, there are five 5-cent coins. So, for every three 10-cent coins, we can think of it as having one set of three 10-cent coins and five 5-cent coins.
Now, let's look at the number of 5-cent coins. The problem tells us that there are x 5-cent coins in the collection.
So, for every set with three 10-cent coins, there are five 5-cent coins. Therefore, the number of sets we have is x/5.
If there are x/5 sets with three 10-cent coins, then the total number of 10-cent coins would be 3 times x/5, which can be written as 3(x/5).
Now, let's add the number of 5-cent coins, which is x, to the number of 10-cent coins. The value of each 10-cent coin is 10 cents and the value of each 5-cent coin is 5 cents.
Therefore, the algebraic expression for the total value of the coins is:
10(3(x/5)) + 5(x)
Simplifying it further, we get:
30x/5 + 5x
And if we combine like terms, it becomes:
6x + 5x
So the final algebraic expression for the total value of the coins is:
11x
And there you go! The total value of the coins can be represented by the expression 11x. Now, go out and collect those coins! Keep the change, my friend! 😉
Let's break down the problem step by step:
Step 1: Define the variables.
Let's define "x" as the number of 5-cent coins in the collection.
Step 2: Determine the number of 10-cent coins.
Based on the given condition, for every three 10-cent coins, there are five 5-cent coins. This means that the number of 10-cent coins is (3/5) times the number of 5-cent coins, which can be expressed as (3/5)*x.
Step 3: Calculate the total value of the coins.
The value of a 10-cent coin is 10 cents, and the value of a 5-cent coin is 5 cents. The total value of the coins can be calculated by multiplying the number of 10-cent coins with their value and adding it to the number of 5-cent coins multiplied by their value.
(10 * (3/5) * x) + (5 * x)
So, the algebraic expression for the total value of the coins is:
10 * (3/5) * x + 5 * x
To find the total value of the coins, we need to determine the number of 10-cent coins in the collection.
The ratio given is that for every three 10-cent coins, there are five 5-cent coins. This can be written as:
(5 cent coins) / (10 cent coins) = 5/3
Since we know that there are x 5-cent coins in the collection, the number of 10-cent coins can be determined by multiplying x by the reciprocal of the ratio:
(10 cent coins) = x * (3/5)
Now, we can determine the total value of the coins by multiplying the number of each type of coin by their respective values:
Total value = (10 cent coins) * 10 cents + (5 cent coins) * 5 cents
Substituting the expression for the number of 10-cent coins:
Total value = (x * (3/5)) * 10 cents + x * 5 cents
Simplifying further, we can distribute the 10 cents across the expression:
Total value = (3/5) * 10 * x cents + 5 * x cents
Finally, we can simplify the expression:
Total value = 6x cents + 5x cents
Combining like terms, we get the final algebraic expression:
Total value = 11x cents
I would have defined x as the number of 10cent coins.
By defining the smallest quantity with your variables, usually fractions can be avoided.
But, anyway....
number of 5 cent coins ---- x
number of 10 cent coins ---x/3
value = 5x + 10x/3