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?

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]

Аноним Аноним · Answer 2 · 2022-02-11T11:34:30+01:00

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]