Question

A restaurant sold 20 gift certificates a total of $650. If they only sell $25 and $50 gift certificates,  how many $25 certificates did they sell?​

Answer 1

14 $25 gift certificates

Explanation:

For simplicity, I've included my work on paper to accompany my explanation.

We can create an equation set of:

`\left \{ {{a + b = 20} \atop {25a + 50b = 650}} \right.`

Where:

• "a" is the quantity of $25 gift certificates
• "b" is the quantity of $50 gift certificates

In this case, we'll use the method of elimination. For starters, we start off by multiplying the 1st equation by 25 to get:

25a + 25b = 500

Next, we'll subtract that answer from the second equation to get:

25b = 150 or b = 6

Now that we have the number of $50 gift certificates, we can plug that number back into the original first equation and get the following:

a = 14 or 14 $25 gift certificates

Hopefully, this helps!

Answer 2

They sold 14 $25 certificates.

Explanation:

System of Equations. To work through this, we will need two equations.

x : number of $25 gift certificates

y : number of $50 gift certificates

The total number of gift certificiates is 20, so the equation we create is:

x + y = 20

They sold the certificates for a total of $650, so we can create the equation:

25x + 50y = 650

The 25 represents the cost for an x number of ceriticates, and the 50 represents the cost for the y number of certificates.

To solve a system of equations, we can use either substitution or elimination. Here, we will use substitution.

x + y = 20

x = 20 - y

25x + 50y = 650

25(20 - y) + 50y = 650

500 - 25y + 50y = 650

500 + 25y = 650

25y = 150

y = 6

Substitute y in for one of the previous equations

x + y = 20

x + 6 = 20

x = 14

They sold 14 $25 certificates and 6 $50 dollar certificates.