Question

Mr Thomsen is buying two types of gift cards to give as prizes to employees at a company meeting. He will buy restaurant gift cards that each cost 50$. He will also buy movie theater gift cards that each cost 20$. He has 450 $ to buy a total of 15 gift cards. how many of each type of gift card can Mr Thomsen buy?

Answer 1

Answer:

$\left \{ {{y=10} \atop {x=5}} \right.$  $\left \{ {{y=11} \atop {x=4}} \right.$ $\left \{ {{y=12} \atop {x=3} \right.$ $\left \{ {{y=14} \atop {x=1}} \right.$

x-restaurant gift cards ;

y-movie theater gift cards

Step-by-step explanation:

x+y=15

50x+20y≤450

$\left \{ {{x\leq 5} \atop {y\geq 10}} \right.$

so,$\left \{ {{y=10} \atop {x=5}} \right.$  $\left \{ {{y=11} \atop {x=4}} \right.$ $\left \{ {{y=12} \atop {x=3} \right.$ $\left \{ {{y=14} \atop {x=1}} \right.$

Answer 2

Mr. Thomsen can by 5 restaurant cards and 10 movie theater gift cards

System of equations

When there are multiple unknowns and providing necessary information to set up solutions in those unknowns, systems of equations are being used to solve applications.

How to determine the each type of gift card Mr. Thomsen buy?

Consider $x$ as the number of restaurant gift cards.

Let's take $y$ as the numbers of movie theaters gift card.

The cost of each restaurant gift cards is 50$

The cost of each movie theater gift cards is 20$

He has 450$ to spend on 15 gift cards.

Therefore, the system of equation to find the each type of gift card will be:

$50x+20y=450$

How to find the value of $x$ :

Here, we know that : $x+y=15$

So, the value of $x$ will be:

$x=15-y$

$50(15-y)+20y=450$    

Expand the equation

$750-50y+20y=450$

Add similar elements

$-50y+20y=-30y$

Therefore, the equation will be:

$750-30y=450$

Then subtract 750 from both sides as follow:

$750-30y =450-750$

$-30y=-300$

Simplify the equation:

$-30y=-300$

Divide the both sides by $-30$

$\frac{-30y}{-30} =\frac{-300}{-30}$

Simplify:

$y=10$

Therefore the value of $x$ will be:

$x=15-10$

$x=5$

Therefore, Mr. Thomsen can by 5 restaurant cards and 10 movie theater gift cards.

To learn more about How to solve the System of equations here: https://brainly.com/question/15412