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Darlene is making a quilt that has alternating stripes of regular quilting fabric and sateen fabric. She spends $76 on a total of 16 yards of the two fabrics at a fabric store. Sateen fabric costs $6 per yard and quilting fabric costs $4 per yard. Which system of equations can be used to find the amount x (in yards) of regular quilting fabric and the amount y (in yards) of sateen fabric she purchased?

Darlene is making a quilt that has alternating stripes of regular quilting fabric and sateen fabric She spends 76 on a total of 16 yards of the two fabrics at a class=

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evgeniylevi

Answer:

[tex]\left \{ {{6x+4y=76} \atop {x+y=16}} \right.[/tex]

Step-by-step explanation:

1) if (according to the condition) the amount of quilting is 'x' and the amount of sateen is 'y', then the price of the quilting fabric is 6*x and the price of then sateen fabric is 4*y;

2) the 76$ she spends can be written as 6x+4y=76;

3) total of 16 yards can be written as x+y=16;

4) finally, the required system is:

[tex]\left \{ {{6x+4y=76} \atop {x+y=16}} \right.[/tex]

You can easily arrange the equation just by observing the question .

  • Spend amount is 76 and there is no simplified value of 76 present except the third one .

So Option C is the answer .

Let me find x and y for you.

  • 4x+6y=76--(1)
  • x+y=16--(2)

Eq(2)×4

[tex]\\ \tt\hookrightarrow 4x+4y=64--(3)[/tex]

Subtracting (1) from (3)

[tex]\\ \tt\hookrightarrow -2y=-12[/tex]

[tex]\\ \tt\hookrightarrow y=6[/tex]

Put in eq(2)

[tex]\\ \tt\hookrightarrow x+6=16[/tex]

[tex]\\ \tt\hookrightarrow x=10[/tex]

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