The probability of randomly selecting a red ball from a jar that contains only red, blue, and orange balls is one-quarter. The probability of randomly selecting a blue ball from the same jar is a third. If the jar contains 10 orange balls, find the total number of balls in the jar.
There are only three possible outcomes for the colour of the ball selected. They are red, blue, and orange. We know that the sum of the probabilities of all possible outcomes is one. So we can subtract the sum of one-quarter and one-third from one to find the probability of choosing an orange ball.
To add one-quarter and one-third, we find their common denominator. The lowest common multiple of four and three is 12. So the lowest common denominator of one-quarter and one-third is 12. To make the denominator of the first fraction 12, we multiply by three.
We must do the same to the numerator to ensure the fractions are equivalent. One multiplied by three is three. Similarly, we multiply the denominator and the numerator of the second fraction by four. One multiplied by four is four. Three plus four is seven, so adding these fractions, we get seven twelfths. So the probability of choosing an orange ball is one minus seven twelfths.
One whole is equivalent to twelve twelfths. So we can subtract seven twelfths from twelve twelfths to give us a probability of five twelfths. There are 10 orange balls, and the probability of choosing an orange ball is five twelfths.
If we call the total number of balls in the jar 𝑥, we can use this information to form an equation. We know that five twelfths of the balls is equal to 10. That’s five twelfths of 𝑥 is equal to 10. To solve this equation, we can either multiply by 12 first or divide by five. Let’s divide by five. We get one twelfth 𝑥 is equal to two. We can then multiply both sides of this equation by 12. And we get 𝑥 is equal to 24. Since we said that 𝑥 was the total number of balls in the jar, we’ve calculated the answer. There are 24 balls in the jar.