William H. answered • 04/20/20

Patient and Effective SAT Math and English Tutor

Start by working with the cheapest bike as an equality.

It costs $115. You have $65. You want to know x = the additional money needed to buy a bike. X is the difference between the money you have saved and the price of the least expensive (cheapest) bike in the store. The difference is $115 – $65. So, $115 – $65 = x. Solving, we have x = $50.

So, starting with $65, you can buy the cheapest bike with an additional $50.

If you save any amount more than $50, you can buy the cheapest bike in the store and have money left over. That is, any amount greater than or equal to $50 will allow you to buy a bike. The two relevant equations are:

$115 – $65 = x, which we saw above, and

$115 – $65 < x

What the second equations expresses is that as long as your additional money, x, is greater that the difference between the price of the cheapest bike ($115)and the amount you already have saved ($65), you will be able to buy a bike.

The two equations can be combined as:

$115 – $65 ≤ x, and you have the inequality you need to determine whether a given additional amount of money will allow you to purchase a bike.