### Video Transcript

Scarlett uses two tablespoons
of sugar for every three glasses of lemonade, while Natalie uses three
tablespoons of sugar for every six glasses of lemonade. Who makes the sweeter
lemonade?

We can begin this question by
writing down a ratio of sugar to lemonade for both of the girls. Scarlett used two tablespoons
for every three glasses of lemonade. Therefore, her ratio is two to
three. Natalie used three tablespoons
of sugar for every six glasses of lemonade. So, her ratio is three to
six. One way of comparing two or
more ratios is to write them in the form one to 𝑛. This is known as the unit
ratio. When finding an equivalent
ratio, we must divide or multiply both sides by the same value. Two divided by two is equal to
one. And three divided by two is
equal to 1.5. This means that, for every one
tablespoon of sugar that Scarlett uses, she will fill 1.5 glasses of
lemonade.

Repeating this process for
Natalie, we divide both sides of her ratio by three. The ratio three to six
simplifies to one to two. This means that, for every one
tablespoon of sugar that Natalie uses, she is able to fill two glasses of
lemonade. We’re asked to work out who
makes the sweeter lemonade. This will be the person who has
less glasses per tablespoon of sugar. As Scarlett is only able to
make one and a half glasses of lemonade for one tablespoon of sugar, she makes
the sweeter lemonade.

Had we noticed that Natalie had
double the number of glasses originally than Scarlett, we could’ve used an
alternative method for this question. Multiplying both sides of
Scarlett’s ratio by two gives us a new ratio, four to six. As Scarlett used four
tablespoons of sugar for six glasses of lemonade whereas Natalie only used three
tablespoons, once again, we have proven that Scarlett made the sweeter
lemonade.