Welcome to our second set of practice
SAT Math questions.
These questions can be viewed and downloaded from ck12.org.
"At Bruno's Video World,
"the regular price of a DVD is d dollars.
"How many DVDs can be purchased for x dollars
"when the DVDs are on sale at 20% off regular price?"
So before we solve this problem,
let's think of a simpler problem.
For example, let's say we have a hundred dollars
and the DVDs cost 10 dollars each.
If we let Q be equal to the quantity we can purchase,
we would take the amount of money we have,
a hundred dollars, and divide by the cost per DVD,
which we're saying would be 10 dollars each.
Notice this quotient is equal to 10,
telling us if we have a hundred dollars,
and the DVDs are 10 dollars each,
we can purchase 10 DVDs.
So now we'll apply this reasoning to the given question.
Notice how the problem tells us
we don't have a hundred dollars, we have x dollars.
So to start, we'll replace $100 with x.
Next, you want to find the cost per DVD,
when we're told the DVDs are regularly d dollars each
but they're 20% off.
So if the DVDs normally cost d dollars but they're 20% off,
that means we still have to pay 80%.
So we want to find 80% of d dollars,
which would be equal to 0.8 times d or just 0.8d.
Okay if you want to find 80% of a number,
we convert the percent to a decimal and then multiply.
Which means we going to replace 10 dollars with 0.8d.
So this quotient does tell us
how many DVDs we can purchase from the given information
but notice how looking at our choices,
they're all in fraction form.
So we need to convert this to a fraction.
So for the first step,
we need to recognize that 0.8 is equal to eight tenths
which would simplify to four fifths
since eight and ten share a common factor of two.
So we can write the given quotient as a complex fraction,
or x divided by four fifths times d
or if we want, four d divided by five.
Now remember a fraction bar just represents division,
so we can write this as a division problem,
meaning this is the same as x divided by four d over five.
But normally we write division problems
involving fractions as multiplication problems.
So this is equivalent to
x times the reciprocal of four d over five,
which would be five over four d.
So we put x over one, we can now find this product
which will give us our quantity in fraction form.
Nothing simplifies so we multiply across the top and bottom.
X times five is five x and one times four d is four d.
So the quantity we can purchase
from the given information would be
five x divided by four d.
So looking at our choices,
five x divided by four d is choice e.
So our answer is e.
I hope you found this explanation helpful.