The ratio between the weights of a son and his father is two to seven. Given that the father weighs 119 kilograms, calculate the weight of the son.
We have the ratio two to seven, which is the ratio of the son to the father. And then we’ve been given the weight of the father. Using this ratio, we want to find 𝑠, the weight of the son. One way to do this would be to set this ratio up as a fraction. The ratio of two to seven would become two-sevenths, and the weight of the son to the father would be 𝑠 over 119. And this would be proportional to two-sevenths. They would be equivalent fractions.
We can solve this by finding the cross product. Seven t times 𝑠 must be equal to two times 119. Two times 119 is 238. And if seven times 𝑠 is equal to 238, then we can divide by seven on both sides of the equation. Seven times 𝑠 divided by 𝑠 equals 𝑠, and 238 divided by seven equals 34. What we’re saying is two-sevenths is equal to 34 over 119, which means that the son weighs 34 kilograms.
Before we move on, let’s consider another way to solve this problem. If we take the ratio two to seven and the ratio 𝑠 to 119, we could ask the question, seven times what equals 119? Put another way, we want to know what multiple of seven 119 is. And if we divide 119 by seven, we see that seven goes into 11 one time with a remainder of four. And seven goes into 49 seven times. This means seven times 17 equals 119. And if 119 is 17 times more than seven, because we’re dealing with a ratio and they’re proportional, the son’s weight will be 17 times more than two. And so we can say that the son’s weight 𝑠 will be equal to two times 17, which is 34. And we confirm the son’s weight of 34 kilograms.