Video Transcript
Each box of oranges weighs eight
and three-eighths kilograms. How many boxes are there if they
weigh a total of 50.25 kilograms?
In this question, we are told that
the weight of a single box of oranges is eight and three-eighths kilograms. And we need to determine the number
of boxes that would weigh 50.25 kilograms.
To answer this question, we can
start by noting that two boxes will weigh two times the weight of a single box of
oranges. Three boxes will weigh three times
the weight of a single box. And, in general, 𝑛 boxes will
weigh 𝑛 times the weight of a single box. Therefore, if we say that 𝑛 boxes
weigh 50.25 kilograms, then we must have that eight and three-eighths times 𝑛 is
equal to 50.25.
We want to solve this equation for
𝑛, so we want to isolate 𝑛 on the left-hand side of the equation. To do this, we will start by
converting the weights into rational numbers. We do this by rewriting eight as 64
over eight, 50 as 200 over four, and 0.25 as one-quarter to obtain the equation 67
over eight times 𝑛 is equal to 201 over four.
To solve for 𝑛, we need to divide
both sides of the equation by 67 over eight. This gives us that 𝑛 is equal to
201 over four divided by 67 over eight. To evaluate this division, we can
recall that division by a fraction is the same as multiplying by its reciprocal. So, 𝑎 over 𝑏 divided by 𝑐 over
𝑑 is equal to 𝑎 over 𝑏 multiplied by 𝑑 over 𝑐. So, if we instead multiplied by the
reciprocal of the weight of a box of oranges, we obtain 𝑛 equals 201 over four
multiplied by eight over 67.
We can now evaluate this
multiplication. We will do this by canceling the
shared factor of 67 in the numerator and denominator to obtain a factor of three in
the numerator and the shared factor of four in the numerator and denominator to find
a factor of two in the numerator. This leaves us with three times
two, which we can calculate is six.
It is worth noting that we can
check our answer by checking that six boxes of oranges weigh 50.25 kilograms. To do this, we want to evaluate
eight and three-eighths times six. We can evaluate this product by
multiplying the integer and fractional part of the mixed number by six and adding
the results. We have eight times six plus three
over eight multiplied by six. In the second product, we can
cancel the shared factor of two in the numerator and denominator to obtain
three-quarters times three.
We can now evaluate each
product. We have eight times six is 48 and
three-quarters times three is nine-quarters. Finally, we can convert the
fraction into a decimal and evaluate the sum to see that the weight of six boxes of
oranges is 50.25 kilograms.
