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Francesca bought 27 key chains of two different kinds to make goody bags for her birthday party. Supergirl key chains were $3 and Wonder Woman key chains were $2. She spent $73. How many key chains of each kind did she buy?

Please help me asap!!

Please provide an explanation as well

Thank you!!

Respuesta :

Answers:

19 Supergirl key chains

8 Wonder Woman key chains

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Explanation:

x = number of Supergirl key chains

y = number of Wonder Woman key chains

Francesca bought 27 total, so the two subtotals x and y must add to the grand total 27. The first equation is therefore x+y = 27. We can isolate y to get y = 27-x after subtracting x from both sides. We will use this equation in the step labeled "substitution step", shown below.

The second equation is 3x+2y = 73. The 3x refers to the total amount of money spent on just the Supergirl key chains ($3 a piece, x number of them, 3*x = 3x). Similarly, the 2y refers to the amount of money spent on just the Wonder Woman key chains, as she bought y of them for $2 a piece. In total, the final bill adds to 3x+2y which we are told is $73. That's how we end up with 3x+2y = 73

We will use the substitution property to get rid of the y variable, allowing us to solve for x

3x+2y = 73

3x + 2( y ) = 73

3x + 2(27 - x) = 73 .... substitution step: replace y with 27-x

3x + 2(27) + 2(-x) = 73 .... distribute

3x + 54 - 2x = 73

3x - 2x + 54 = 73

x + 54 = 73

x+54 - 54 = 73 - 54 ... subtract 54 from both sides

x = 19

Francesca bought 19 Supergirl key chains

Use this x value to find y. Go back to y = 27-x

y = 27 - x

y = 27 - 19 ... replace x with 19

y = 8

She also bought 8 Wonder Woman key chains

So the ordered pair solution is (x,y) = (19,8). If you were to graph the two equations x+y = 27 and 3x+2y = 73, then the two lines would cross at the location (19,8)

dsdrajlin

Francesca bought 8 Wonder Woman key chains ($3 each) and 19 Supergirl key chains ($2 each) spending a total of $73.

What is a system of linear equations?

In mathematics, a system of linear equations is a collection of one or more linear equations involving the same variables.

  • Let "s" be the number of Supergirl key chains and "w" the number of Wonder Woman key chains.

  • Francesca bought 27 key chains of two different kinds. The mathematical expression would be:

s + w = 27    

s = 27 - w    [1]

  • Supergirl key chains were $3 and Wonder Woman key chains were $2. She spent $73. The mathematical expression would be:

3 s + 2 w = 73   [2]

  • If we substitute [1] in [2], we get:

3 (27 - w) + 2 w = 73

81 - 3 w + 2 w = 73

w = 8

  • If we input this value in [1], we get:

s = 27 - 8 = 19

Francesca bought 8 Wonder Woman key chains ($3 each) and 19 Supergirl key chains ($2 each) spending a total of $73.

Learn more about linear equations here: https://brainly.com/question/14323743