Video Transcript
Anthony has two containers, A and
B, that contain 3.6 kilograms and 4.8 kilograms of sugar. If he takes one-third and
two-thirds of the sugar in containers A and B, respectively, and places them in C, a
third container, how many kilograms of sugar are in container C?
In this question, we are told that
Anthony takes one-third of the amount of sugar in container A and two-thirds the
amount of sugar in container B and places the sugar into a third container C. We want to determine the mass of
sugar in container C.
To find this value, we will start
by calling 𝑎 the amount of sugar that is originally in container capital A and 𝑏
the amount of sugar that is originally in container capital B. If Anthony takes one-third the
amount of sugar out of container capital A, then he has one-third times 𝑎 kilograms
of sugar. Similarly, if he takes two-thirds
the amount of sugar out of container capital B, then he has two-thirds times 𝑏
kilograms of sugar. Adding these together gives us the
amount of sugar that will be in container capital C, which we will call 𝑐.
To evaluate the expression for the
mass of sugar, we can start by substituting in the values for 𝑎 and 𝑏. We have that one-third times 3.6
plus two-thirds times 4.8 is equal to 𝑐.
By recalling the order of
operations, we note that we now need to evaluate the multiplications. To do this, we recall that we can
do this by writing each of the rational numbers as fractions. We could write the fractions in
simplified form with a denominator of five. However, we will use a denominator
of 10. We have 3.6 is equal to 36 over 10
and 4.8 is equal to 48 over 10. This gives us one-third times 36
over 10 plus two-thirds times 48 over 10 is equal to 𝑐.
We can then evaluate both products
by recalling that we can multiply fractions by multiplying their numerators and
denominators separately. In general, we have that 𝑎 over 𝑏
times 𝑐 over 𝑑 is equal to 𝑎𝑐 over 𝑏𝑑. This then gives us one times 36
over three times 10 plus two times 48 over three times 10 is equal to 𝑐. We can cancel the shared factor of
three in the numerator and denominator so that the denominators of the fractions are
10. This will make conversion back to a
decimal easier. We have one times 12 over 10 plus
two times 16 over 10 equals 𝑐.
We can now evaluate each of the
products to obtain 12 over 10 plus 32 over 10 is equal to 𝑐. We can now see that we are adding
two fractions together with the same denominator. So we just add the numerators to
get 12 plus 32 over 10. We can evaluate the sum to get 44
over 10, which we can convert into a decimal to see that there is 4.4 kilograms of
sugar in container C.
