All categories

2 years ago

To make a quilt, a quilter is buying fabric in two colors, blue and green.

Mathematics

1 answer:

egoroff_w [7]2 years ago

3 0

Answer:

<h2>3.375yards of blue fabric </h2><h2>6.125yards of green fabric</h2>

Step-by-step explanation:

step one:

given data

blue fabric costs $9 a yard.

green fabric costs $13 a yard.

Let x represent the number of blue yards of fabric purchased and

let y represent the number of green yards of fabric purchased.

Step two:

The quilter needs at least 9.5 yards of fabric in total.

x+y>=9.5--------1

The quilter can spend up to $110 on fabric.

9x+13y<=110----2

from equation

x+y>=9.5

x=9.5-y

put x=9.5-y in equation 2 we have

9(9.5-y)+13y<=110----2

85.5-9y+13y=110

4y=110-85.5

4y=24.5

y=24.5/4

y=6.125

put y=6.125 in x=9.5-y to find x

x=9.5-6.125

x=3.375

Hence the quilt can purchase

3.375yards of blue fabric

6.125yards of green fabric

You might be interested in

8. The loudness of a sound depends on_____. A. The width of the wave B. The brightness of the wave C. The length of a sound wave

cupoosta [38]

Answer:

Step-by-step explanation:

loudness depends on the amplitude or height of the sound waves

5 0

2 years ago

Kellen bought new fish for her home aquarium. She bought 4 turquoise guppies and 3 sunburst tetra GLO fish and spent a total of

FromTheMoon [43]

Answer: A single turquoise guppy costs $3.69

Step-by-step explanation:

Let us use "x" to represent the amount a single turquoise is sold and use "y" to represent that of the Glo fish.

Since Kellen bought 4 guppies and 3 glo fishes for $41.73:

4x + 3y = 41.73 --------eqn 1

Similarly, Danielle purchased 3 guppies and 5 Glo fish for $56.02:

Therefore 3x + 5y = $56.02 -----eqn2

The 2 equations are;

4x + 3y = 41.73 (eqn 1)

3x + 5y = 56.02 (eqn 2)

We then solve the simultaneous equations using substitution method:

From eqn 1,

4x + 3y = 41.73

4x = 41.73 - 3y

x = (41.73 - 3y)/4

Substitute x for (41.73 - 3y)/4 in eqn2.

3[(41.73 - 3y)/4 + 5y = 56.02

11y + 125.19 = 224.08

11y =98.89

y = 98.89/11

y = $8.99

So, 1 Glo fish costs $8.99

Then, substitute "y" for 8.99 in equation 1

4x + (3×8.99) = 41.73

4x + 26.97 = 41.73

4x = 41.73 - 26.97

4x = 14.76

x = 14.76/4

x = $3.69

Therefore 1 turquoise guppy costs $3.69

5 0

2 years ago

I beg someone to answer ive posted this 3 times and im still not sure how to do it.....

Anni [7]

Answer:

D) 3 X 10⁷

Step-by-step explanation:

<u>Estimated days:</u>

Jan 2000 to June 2001 = 1.5 years = 365*1.5 days ≈ 548 days

1 day = 24 hours = 24*60 minutes = 24*60*60 seconds =

86400 seconds

548 days = 548 * 86400 seconds =

47347200 ≈ 4.7*10⁷

Best estimate is D) 3 X 10⁷

8 0

2 years ago

In a given year, the population of Metro City is 7420, and the population is decreasing by 152 people per year. The population o

Anit [1.1K]

Answer:

The correct option is D.

Step-by-step explanation:

Let <em>x</em> denote the years.

The information provided is:

The population of Metro City is 7420.
The population is decreasing by 152 people per year.
The population of Smallville is consistently 1200 less than half of Metro City.

From the provided data derive the equation for the population of Smallville <em>x</em> years after as follows:

$Y = [\frac{1}{2}\cdot (7420-152x)]-1200$

The population of Smallville is 2282 after <em>x</em> years.

Compute the value of <em>x</em> as follows:

$2282= [\frac{1}{2}\cdot (7420-152x)]-1200$

$\frac{7420-152x}{2}=2282+1200\\\\7420-152x=3482\times 2\\\\152x=7420-6964\\\\152x=456\\\\x=3$

Thus, the time it will take for Smallville's population to reach 2282 is 3 years.

The correct option is D.

7 0

2 years ago

Jack has $37 and saves $6.50 per week. Diane has $9 and saves $8.25 per week. Define a variable, then write and solve an equatio

Aleks [24]

Answer:

Defining variable: x = per week

Equation: 37 + 6.5x = 9 + 8.25x

Answer: 16 weeks

Step-by-step explanation:

x = per week

Jack:

37 + 6.5x

Diane:

9 + 8.25x

Equation:

37 + 6.5x = 9 + 8.25x

-1.75x = -28

x = 16

5 0

2 years ago