1. I've posted this question before (once, the other post wasn't me)and I have still got no help.
Peg spends $7.50 a week for grapefruit. When grapefruit are out of season, she gets 1 fewer grapefruit than when they are in season. If the price decreases by $3 per dozen in season, how many dollars will it cost to buy a dozen grapefruit out of season?
Let the price per dozen in season be $x
let the price per dozen out of season be $(x+3)
So in season for $7.50 she can buy 7.5/x dozen
or 90/x grapefruits
Out of season for $7.50 she can buy 7.5/(x+3) dozen or 90/(x+3) grapefruits
so 90/x - 90/(x+3) = 1
multiply by x(x+3)
90(x+3) - 90x = x(x+3)
expand and simplify
x^2 + 3x - 270 = 0
(x+18)(x-15) = 0
x = -18 or x = 15 , but clearly x > 0
price out of season was defined as x+3
so out of season they sold at $18 per dozen, WOW!
check:
in season she could buy 7.5/15 = .5 dozen or 6 grapefruits
out of season she could buy 7.5/18 or .4166667 dozen or 5 grapefruits
is 6-5 = 1 ? YES
To determine the cost of buying a dozen grapefruit out of season, we first need to understand the information given in the question.
1. Peg spends $7.50 a week for grapefruit. This establishes the weekly cost of buying grapefruit.
2. When grapefruit are out of season, she gets 1 fewer grapefruit than when they are in season. This means that the number of grapefruit Peg buys in a week varies depending on the season.
3. The price of grapefruit decreases by $3 per dozen in season. This gives us information about the price difference between in-season and out-season grapefruit.
Now let's break down the problem step by step:
Step 1: Determine the price of a dozen grapefruit in season
Since Peg spends $7.50 per week on grapefruit, we can divide this amount by the number of grapefruit she gets in a week to find the price per fruit. Let's call the number of grapefruit she gets in-season as "x".
So, the price per fruit in season = $7.50 / x
Now, since the price decreases by $3 per dozen (which is 12 fruit) in season, the price per fruit out of season will be:
Price per fruit out of season = (Price per fruit in season - $3)
Step 2: Calculate the cost of buying a dozen grapefruit out of season
Since a dozen contains 12 fruit, we can multiply the price per fruit out of season by 12 to find the cost of buying a dozen grapefruit out of season.
Now that we have established the steps, we can go ahead and calculate the answer:
1. Determine the price of a dozen grapefruit in season by substituting the value of x (the number of grapefruit she gets in a week in-season) into the equation: Price per fruit in season = $7.50 / x
2. Calculate the price per fruit out of season by subtracting $3 from the price per fruit in season: Price per fruit out of season = (Price per fruit in season - $3)
3. Multiply the price per fruit out of season by 12 to calculate the cost of buying a dozen grapefruit out of season.
Follow these steps, and you will be able to find the answer to the problem.