Answer :
To solve this problem, we need to determine the number of green counters in a bag that contains a total of 56 counters. The counters in the bag are only green and blue, and their numbers are in the ratio of 1:3 (green:blue).
Here's how you can approach solving this step-by-step:
1. Understand the Ratio: The ratio given is 1:3, which means for every 1 green counter, there are 3 blue counters. Together, these form a group of 4 parts (1 part green + 3 parts blue).
2. Calculate Total Parts: With the ratio 1:3, there are a total of 4 parts. This means the counters are divided into 4 equal sections based on their colors.
3. Determine Value of One Part: Since the entire collection of counters (56 counters) is divided into 4 parts, to find out how many counters make up each part, you divide the total number by the number of parts:
[tex]\[
\text{One part} = \frac{56}{4} = 14
\][/tex]
4. Find Green Counters: According to the ratio, green counters make up 1 part out of the total 4 parts. Given each part is 14 counters:
[tex]\[
\text{Green counters} = 1 \times 14 = 14
\][/tex]
There was an error in a previous calculation that led to getting a fractional answer, but correcting this using logical steps shows that the number of green counters in the bag is 14.
Here's how you can approach solving this step-by-step:
1. Understand the Ratio: The ratio given is 1:3, which means for every 1 green counter, there are 3 blue counters. Together, these form a group of 4 parts (1 part green + 3 parts blue).
2. Calculate Total Parts: With the ratio 1:3, there are a total of 4 parts. This means the counters are divided into 4 equal sections based on their colors.
3. Determine Value of One Part: Since the entire collection of counters (56 counters) is divided into 4 parts, to find out how many counters make up each part, you divide the total number by the number of parts:
[tex]\[
\text{One part} = \frac{56}{4} = 14
\][/tex]
4. Find Green Counters: According to the ratio, green counters make up 1 part out of the total 4 parts. Given each part is 14 counters:
[tex]\[
\text{Green counters} = 1 \times 14 = 14
\][/tex]
There was an error in a previous calculation that led to getting a fractional answer, but correcting this using logical steps shows that the number of green counters in the bag is 14.
