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In a pond, the ratio of toads to frogs was [tex]3:10[/tex].

9 more frogs then entered the pond, and the ratio of toads to frogs became [tex]3:11[/tex].

Work out how many toads are in the pond.


Sagot :

To solve this problem, we need to determine the number of toads in the pond. Let's follow the steps to find the solution:

1. Establish the initial ratio:
- We are given that the initial ratio of toads to frogs is [tex]\( 3:10 \)[/tex].
- Let the initial number of toads be [tex]\( 3x \)[/tex] and the number of frogs be [tex]\( 10x \)[/tex].

2. Account for the change:
- We are informed that 9 more frogs enter the pond.
- Therefore, the number of frogs becomes [tex]\( 10x + 9 \)[/tex].

3. Set up the new ratio:
- The new ratio of toads to frogs becomes [tex]\( 3:11 \)[/tex].
- Using our variables, the number of toads remains [tex]\( 3x \)[/tex] and the number of frogs is now [tex]\( 10x + 9 \)[/tex].

4. Set up the ratio equation:
- The new ratio can be formed into an equation:
[tex]\[ \frac{3x}{10x + 9} = \frac{3}{11} \][/tex]

5. Solve the equation for [tex]\( x \)[/tex]:
- Cross multiply to solve for [tex]\( x \)[/tex]:
[tex]\[ 11 \cdot 3x = 3 \cdot (10x + 9) \][/tex]
- Simplify:
[tex]\[ 33x = 30x + 27 \][/tex]
- Isolate [tex]\( x \)[/tex]:
[tex]\[ 33x - 30x = 27 \][/tex]
[tex]\[ 3x = 27 \][/tex]
[tex]\[ x = 9 \][/tex]

6. Calculate the number of toads:
- Recall that the number of toads is [tex]\( 3x \)[/tex].
- Substitute [tex]\( x = 9 \)[/tex]:
[tex]\[ 3 \times 9 = 27 \][/tex]

Therefore, the number of toads in the pond is [tex]\( 27 \)[/tex].
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