A piggy bank with only pennies and nickels has 28 nickels for every 52 pennies. What percent of the coins are nickels? solve this problem using
a. bar diagram
b. percent equation
28/80 = 0.35 = 35%
To solve this problem using a bar diagram, you can draw two bars to represent the number of pennies and nickels. Since we know that there are 28 nickels for every 52 pennies, we can represent this relationship as a fraction:
Number of nickels / Number of pennies = 28 / 52
To make it easier to work with, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4:
Number of nickels / Number of pennies = 7 / 13
Now, let's draw the bar diagram. Divide the diagram into two equal parts and label them as "nickels" and "pennies". Since we have the ratio of 7 nickels to 13 pennies, we can represent this by shading 7 out of the total 13 parts in the "nickels" section of the diagram.
To find the percent of coins that are nickels, we need to determine the fraction of nickels out of the total number of coins. Since we are only given the information about pennies and nickels and not the total number of coins, we don't have enough information to determine the exact percent.
However, if we assume that the total number of coins is 100, we can calculate the percent using the proportion:
7 nickels / 13 coins = x percent / 100
Cross multiplying, we have:
7 * 100 = 13 * x percent
700 = 13x
x = 700 / 13
x ≈ 53.85
Therefore, approximately 53.85% of the coins are nickels.
Now let's solve the problem using the percent equation.
We know that there are 28 nickels for every 52 pennies. To find the percentage of nickels, we can use the formula:
(Percent / 100) = Part / Whole
Let's assign variables to the parts of the equation:
- Let x be the percentage of nickels.
- Let 28 be the part (number of nickels).
- Let 52 be the whole (total number of coins).
Using the percent equation, we have:
(x / 100) = 28 / 52
Now we can solve for x by cross multiplying:
52x = 2800
Divide both sides by 52:
x = 2800 / 52
x ≈ 53.85
Again, we find that approximately 53.85% of the coins are nickels.