Question

At a supermarket, the price of yellow onions dropped from $0.58 per pound to $0.43 per pound.

(a)What is the percent decrease in the price of onions? (Round your answer to one decimal place.)
_____%

(b)Tomatoes are expected to undergo the same percent decrease in price. If they currently sell for $1.03 per pound, what will be the new price (in $ per lb) of tomatoes? (Round your answer to two decimal places.)
$ _____per lb

Answer 1

Answer:

a. 25.9%  b. $.76 per pound

Step-by-step explanation:

For part a. the formula for percent decrease is

% dec = $\frac{orig-new}{orig}*100$

We are solving for % dec.  Filling in:

% dec = $\frac{.58-.43}{.58}*100$ simplifies to

% dec = $\frac{.15}{.58}*100$ which gives us, rounded to one decimal place:

% dec = 25.9%

For part b. we are going to use that percent decrease and fit it into a new equation to solve for the new price of tomatoes when we know the original price.  Filling in:

$25.9=\frac{(1.03-new)}{1.03}*100$ which could be written instead as

$25.9=\frac{(1.03-new)100}{1.03}$

Now you can see what will happen on the right when we divide by 100...they cancel out.  That looks like this, when we divide both sides by 100, as we must because this is an equation:

$\frac{25.9}{100}=\frac{(1.03-new)100}{(1.03)(100)}$

Simplifying on both sides:

$.259=\frac{1.03-new}{1.03}$

Now we will multiply both sides by 1.03:

.26677 = 1.03 - new  and

-.76323 = -new so

the new price is .76 per pound