Math Problem Statement

The odds on​ (against) your bet are

11

to

If you bet

​$6363

and​ win, how much will you​ gain?

Question content area bottom

Part 1

​$enter your response here

​(Type an integer or a​ decimal.)

Solution

The odds given are 11 to 77, which means for every 11 units you win, you must risk 77 units. To calculate how much you will gain if you bet $6363 and win, we can use the ratio of the odds.

The formula to calculate the gain is:

Gain=bet amountrisked units×units won\text{Gain} = \frac{\text{bet amount}}{\text{risked units}} \times \text{units won}

Here:

  • Bet amount = $6363
  • Risked units = 77
  • Units won = 11

Substitute into the formula:

Gain=636377×11\text{Gain} = \frac{6363}{77} \times 11

Gain=82.67×11=909.37\text{Gain} = 82.67 \times 11 = 909.37

Therefore, if you bet $6363 and win, you will gain approximately $909.37.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

  1. What would happen to the gain if the odds were 15 to 85 with the same bet?
  2. How do we calculate potential losses with odds like these?
  3. How do fractional and decimal odds relate to "odds on" or "odds against"?
  4. If you increase the bet to $10,000, how does the gain change?
  5. How are payouts in odds calculated for various sports betting scenarios?

Tip: Always check whether odds are quoted as "odds on" or "odds against" to know if the payout is larger or smaller than the initial stake.

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Betting Odds

Formulas

Gain = (bet amount / risked units) × units won

Theorems

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Suitable Grade Level

Grades 9-12