Question

The store sells gift cards in preset amounts. You can purchase gift cards for $10 or $15. You have spent $280 on gift cards. Write an equation in standard form to represent this situation. What are the three combination of gift cards you could have purchased? 1. 18 gift cards for $10 and 1 gift card for $15; 4 gift cards for $10 and 16 gift cards for $15; and 16 gift cards for $10 and 8 gift cards for $15.2. One gift card for $10 and 18 gift cards for $15; 4 gift cards for $10 and 16 gift cards for $15.; 16 gift cards for $10 and 8 gift cards for $15.3. 18 gift cards for $10 and 0 gift cards for $15; 4 gift cards for $15 and 16 gift cards for $10; 16 gift cards for $15 and 8 gift cards for $10.4. 0 gift cards for $10 and 18 gift cards for $15; 4 gift cards for $10 and 16 gift cards for $15; 16 gift cards for $15 and 8 gift cards for $10.

Answer 1

STEP-BY-STEP EXPLANATION

What to find? Develop a standard form representing the situation.

Given parameters

Let the gift card sold for $10 be x

Let the gift cards sold for $15 be y

The total amount spent on the gift cards is $280

The equation representing the situation can be expressed as

$10 x number of x gift cards + $15 x number of y gift cards = Total cost of cards purchased

$\begin{gathered} \text{Hence, the equation in standard form is expressed as} \\ 10x\text{ + 15y} \end{gathered}$

Note: The total amount of card purchased is $280

To find the three combinations of gift cards you could have purchased, we need to find the cost of each gifts-card that will give us a total of $280

Hence, we have:

Total cost = $10 x number of x gift cards + $15 x number of y gift cards

Mathematically, this can be expressed as

$10x\text{ + 15y = 280}$

Considering the second option, we will substitute the value of x and y into the above equation

$\begin{gathered} \text{The equation generated is } \\ 10x\text{ + 15y = 280} \\ \text{for x = 1 and y = 18} \\ \text{Substitute the values into the equation} \\ 10(1)\text{ + 18(15) = 280} \\ 10\text{ + 270 = 280} \\ 280\text{ = 280} \\ \text{Hence, the above condition satisfied the equation} \end{gathered}$

When x = 4 and y = 16

$\begin{gathered} 10x\text{ + 15y = 280} \\ 10(4)\text{ + 15(16) = 280} \\ 40\text{ + 240 = 280} \\ 280\text{ = 280} \\ \text{The above condition satisfied the equation} \end{gathered}$

When x = 16 and y = 8

$\begin{gathered} 10x\text{ + 15y = 280} \\ 10(16)\text{ + 15(8)=280} \\ 160\text{ + 120 = 280} \\ 280\text{ = 280} \\ \text{The above condition satisfied the equation} \end{gathered}$

Therefore, three combinations of gift cards you could have purchased is considered in option 2