The cheapest bike in at the store is $115. You have $65 saved up. How much more do you need to save before you can buy a bike from this store?

Question

1. Write an inequality to model the scenario
2. Identify the variable or unknown value. (what are you looking for)
3. Identify the operation 
4. Identify the total 
5. Determine the inequality sign
6. Solve the equation to find the unknown value

 

1. If you saved $100 more, can you buy a bike?

Answer 1

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.