Jay can buy a stereo either online or at local store. If he buys online , he gets a 15% discount, but has to pay a $12 shipping fee. At the local store, the stereo is not on sale, but there is no shipping fee. For what regular price is it cheaper for Jay to buy the stereo online?
Let's say the regular price of the stereo is x dollars.
If Jay buys the stereo online, he will get a 15% discount, which means he will pay 85% of the regular price.
So, Jay will pay 0.85x dollars if he buys the stereo online.
In addition, he has to pay a $12 shipping fee.
So, the total cost for Jay to buy the stereo online is 0.85x + $12.
On the other hand, if Jay buys the stereo at the local store, he will pay the regular price of x dollars.
To determine when it is cheaper for Jay to buy the stereo online, we need to compare the costs.
To determine if it is cheaper for Jay to buy the stereo online, we need to compare the total cost of buying it online with the total cost of buying it at the local store.
Let's assume the regular price of the stereo is X dollars.
If Jay buys the stereo online, he gets a 15% discount, so he would pay (100% - 15%) = 85% of the regular price. This can be calculated as 0.85*X.
In addition to the discount, Jay would also have to pay a $12 shipping fee. So the total cost of buying the stereo online would be 0.85*X + $12.
On the other hand, if Jay buys the stereo at the local store, he would pay the full regular price, which is X dollars.
To determine when it is cheaper to buy the stereo online, we need to find out when the total cost of buying it online is less than the total cost of buying it at the local store.
So, we need to solve the following inequality:
0.85*X + $12 < X
Let's solve for X:
0.85*X - X < -$12
-0.15*X < -$12
X > -$12 / -0.15
X > $80
Therefore, for a regular price greater than $80, it is cheaper for Jay to buy the stereo online.
To determine which option is cheaper for Jay, we need to compare the total cost of buying the stereo online with the regular price of buying it at the local store.
Let's denote the regular price of the stereo as "x".
If Jay buys the stereo online, he will get a 15% discount. So, the discounted price would be 85% of the regular price, or 0.85x.
However, Jay will also need to pay a $12 shipping fee in addition to the discounted price. Hence, the total cost of buying the stereo online would be 0.85x + $12.
On the other hand, if Jay buys the stereo at the local store, he would have to pay the full regular price, which is x.
To determine when it is cheaper to buy online, we need to compare the total cost of buying online (0.85x + $12) with the regular price of buying at the local store (x).
Setting up an inequality, we have:
0.85x + $12 < x
Now, let's solve this inequality to find the regular price (x) at which it is cheaper to buy the stereo online:
0.85x + $12 < x (Subtract 0.85x from both sides)
$12 < 0.15x (Divide both sides by 0.15)
$12 / 0.15 < x
80 < x
Therefore, for any regular price (x) greater than $80, it is cheaper for Jay to buy the stereo online.