The ratio of gummy bears to gummy warms in a bag of candy is 5:4 if there are 160

Answer 1

To find the number of gummy bears and gummy worms in a bag of candy given the ratio of gummy bears to gummy worms is 5:4, you can follow these steps:

1. Let the common multiplier be \( x \).

2. So, the number of gummy bears can be represented as \( 5x \) and the number of gummy worms as \( 4x \).

3. According to the problem, the total number of gummy bears and gummy worms is 160. So, we can set up the equation:

   \[ 5x + 4x = 160 \]

4. Combine like terms:

   \[ 9x = 160 \]

5. Now, solve for \( x \):

   \[ x = \frac{160}{9} \approx 17.78 \]

6. Find the number of gummy bears and gummy worms by substituting \( x \) back into the expressions:

   • Gummy Bears: \( 5x \approx 5 \times 17.78 \approx 88.89 \) (rounding would mean approximately 89)
   • Gummy Worms: \( 4x \approx 4 \times 17.78 \approx 71.11 \) (rounding would mean approximately 71)

However, since the quantities of gummy bears and gummy worms must be whole numbers, they can be best expressed as follows based on the ratio.

To count the integer quantities in a 5:4 ratio with an approximate total of 160:

• The total parts in the ratio is \( 5 + 4 = 9 \).

To find the value of each part:

• Each part is \( \frac{160}{9} \approx 17.78 \).

Calculating specifically:

• Gummy Bears: \( 5 \times 17.78 \approx 89 \)
• Gummy Worms: \( 4 \times 17.78 \approx 71 \)

Final counts based on whole numbers with proper rounding could give you:

• Gummy Bears: 90
• Gummy Worms: 70

Thus, the precise whole number portions should be adjusted to sum to 160 in ratios that hold closely to the original given proportions.

To achieve whole numbers which best fit the 5:4 ratio from the total of 160, the answer is:

• Gummy Bears: 90
• Gummy Worms: 70

These quantities reflect the 5:4 ratio while summing perfectly to 160.