Question

Katie is buying souvenir gifts for her big family back home. She wants to buy everyone either a key chain or a magnet. The magnets are on sale for 60 cents each and the key chains cost $2 each. She must purchase at least 36 gifts but has to spend less than $40. Let x represent the amount of key chains and y represent the amount of magnets. Model the scenario with a system of inequalities.

Answer 1

Answer: The system of inequalities will be

`x+y\geq 36\\\\2x+06y<40`

Explanation:

Since we have given that

Cost of each key chains = $2

Cost of each magnet = 60 cents = $0.6

Let the amount of key chains be 'x'.

Let the amount of magnets be 'y'.

According to question,

She must purchase at least 36 gifts, so it becomes,

`x+y\geq 36`

Similarly, she has to spend less than $40. So, it becomes,

`2x+0.6y<40`

Hence, the system of inequalities will be

`x+y\geq 36\\\\2x+06y<40`

Answer 2

1. 
   `x+y\ge 36`
2. 
   `2x+0.6y<40`

Explanation:

Let us assume that, x is the amount of key chains and y is the amount of magnets.

As Katie must purchase at least 36 gifts i.e she can buy any number of gifts greater or equal to 36, so

`x+y\ge 36` ----------------------------1

Price of the magnet is 60 cents or $0.60 each and the key chains cost $2 each. As she has to spend less than $40 i.e she can spend any amount less than 40.

`2x+0.6y<40` -------------------------2