Question

A vendor at a craft show sold items
for $4.50, $6.00, and $7.50. Altogether,
the vendor sold 87 items for a total of
$489. The vendor sold 5 more items for
$6.00 than for $7.50. Which system of
equations could you use to determine
how many of each item were sold?
a.
⎧
⎪ ⎨ ⎪
⎩

x + y + z = 489
z = y + 5
4.5x + 6y + 7.5z = 87

b.
⎧
⎪ ⎨ ⎪
⎩

x + y + z = 489
y = z + 5
4.5x + 6y + 7.5z = 87

c.
⎧
⎪ ⎨ ⎪
⎩

x + y + z = 87
y = z + 5
4.5x + 6y + 7.5z = 489

d.
⎧
⎪ ⎨ ⎪
⎩

x + y + z = 87
z = y + 5
4.5x + 6y + 7.5z = 489

Answer 1

The system of equations that could be used to determine how many of each item were sold is:

C.

x + y + z = 87

y = z + 5

4.5x + 6y + 7.5z = 489

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

• Variable x: Number of items sold for $4.50.

• Variable y: Number of items sold for $6.00.

• Variable z: Number of items sold for $7.50.

87 items in total were sold, hence:

x + y + z = 87.

The total earned was of $489, hence:

4.5x + 6y + 7.5z = 489.

The vendor sold 5 more items for $6.00 than for $7.50, hence:

y = z + 5.

These three equations are given in option C.

More can be learned about a system of equations at https://brainly.com/question/24342899

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