Question Video: Finding the Unknown in a Proportion Mathematics • 7th Grade

If 7/๐‘ฅ = 42/78, find the value of ๐‘ฅ.

02:26

Video Transcript

If seven over ๐‘ฅ equals 42 over 78, find the value of ๐‘ฅ.

Weโ€™ve been given an equation that describes the proportion between different values. Weโ€™re told that the proportion of seven to ๐‘ฅ is equal to the proportion of 42 to 78. And so there are a number of ways we can answer this question. The first is just to rearrange and make ๐‘ฅ the subject. Alternatively, weโ€™ll think about what it means when things are in proportion to one another.

If seven is in the same proportion to ๐‘ฅ as 42 is to 78, then we could say that seven times some constant ๐‘ gives us the value of ๐‘ฅ, where that constant of ๐‘ also holds in the equation 42 times ๐‘ equals 78. With our second equation, if we divide through by 42, we get ๐‘ equals 78 divided by 42. Replacing ๐‘ in our first equation with 78 over 42, and we get seven times 78 over 42 equals ๐‘ฅ.

Next, we can simplify this equation. We notice both seven and 42 have a factor of seven. Seven divided by seven is one. And 42 divided by seven is six. So our equation becomes one times 78 over six equals ๐‘ฅ. In other words, ๐‘ฅ is 78 divided by six. Then weโ€™ll calculate the value of ๐‘ฅ by using the bus stop method. We begin by asking how many sixes make seven. Well, itโ€™s seven with a remainder of one. Next, how many sixes make 18? Itโ€™s three. So 78 divided by six is 13, meaning ๐‘ฅ must be equal to 13.

Remember though, we said this wasnโ€™t the only way to solve the problem. We could have solved just like solving any normal equation. Letโ€™s take the equation seven over ๐‘ฅ equals 42 over 78. Since we have purely fractional expressions on both sides, we can find the reciprocal of both sides of this equation. So on the left-hand side, thatโ€™s ๐‘ฅ over seven. And on the right-hand side, itโ€™s 78 over 42. Then to make ๐‘ฅ the subject, we multiply through by seven. And At this stage, we notice we have the exact same expression as we did earlier. Either way, we found the value of ๐‘ฅ is 13.

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