timothyhenman1 wrote:
For each customer, a yogurt shop charges a cents for the first 5oz of purchased yogurt. Each additional ounce of yogurt costs the customer b cents. What is the value of a?
(1) A customer who buys 10oz of yogurt is charged 10 percent less per ounce than a customer who buys just 5oz of yogurt.
(2) A customer who buys 20oz of yogurt is charged $2.50
Hi,
if we look at the problem,
we have three unknowns, two values/prices and one qty, and one number 5..lets see what does each eq tells us..
(1) A customer who buys 10oz of yogurt is charged 10 percent less per ounce than a customer who buys just 5oz of yogurt.we are given a qty value and a percentage relation to 5..
since they are no numeric values about the two values/price, this statement will give us a ratio of the two values.. insuff
(2) A customer who buys 20oz of yogurt is charged $2.50this eq gives us the QTY and sum of two prices..
so, what we get from this statement is a linear equation between the two prices..... insuff as we still do not know indl prices..
combined we have a linear equation of two variables and the ratio of these two variables...hence SUFF to find the value of two variables...
Lets put this Algebrically too..(1) A customer who buys 10oz of yogurt is charged 10 percent less per ounce than a customer who buys just 5oz of yogurt.(5a+5b)/10=0.9 * a... 5a+5b=9a... or 4a=5b..
a=5b/4... insuff..
(2) A customer who buys 20oz of yogurt is charged $2.505a + 15 b =2.5... insuff..
combined substitute a as 5b/4 in eq formed from statement II...
5(5b/4) + 15b = 2.5..
25b +60b =10..
b= 10/85.... and a can be found.... suff