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3 years ago

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HELP MEEEEEEEEEE Package A contains 3 birthday cards and 2 thank-you notes and costs $9.60. Package B contains 8 birthday cards

and 6 thank-you notes and costs $26.60. If x represents the cost of a birthday card and y represents the cost of a thank-you note, how much does each birthday card cost?{3x+2y=9.6 8x+6y=29.6 a $1.33 b $1.50 c $2.20 d $3.10

2 answers:

STatiana [176]3 years ago

8 0

Answer: The correct option is

(c) $2.20.

Step-by-step explanation: Given that package A contains 3 birthday cards and 2 thank-you notes and costs $9.60. Package B contains 8 birthday cards and 6 thank-you notes and costs $26.60.

Also, x represents the cost of a birthday card and y represents the cost of a thank-you note.

We are to find the cost of each birthday card.

The system of linear equations representing the given situation is given by

$3x+2y=9.60~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\8x+6y=26.60~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Multiplying equation (i) by 3, we have

$3(3x+2y)=3\times9.60\\\\\Rightarrow 9x+6y=28.80~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Subtracting equation (ii) from (iii), we get

$(9x+6y)-(8x+6y)=28.80-26.60\\\\\Rightarrow x=2.20.$

Thus, the cost of each birthday card is $2.20

Option (c) is CORRECT.

hodyreva [135]3 years ago

6 0

Answer:

Each birthday card costs $2.2 ⇒ answer c

Step-by-step explanation:

* Lets explain how to solve the problem

- Package A contains 3 birthday cards and 2 thank-you notes

- It costs $9.60

- Package B contains 8 birthday cards and 6 thank-you notes

- It costs $26.60

- x represents the cost of birthday card and y represents the cost of

thank-you note

* Lets change these information to two equations

∵ x represents the cost of each birthday cards

∵ y represents the cost of each thank-you notes

∵ Bag A contains 3 birthday cards and 2 thank-you notes

∵ Bag A costs $9.60

∴ 3x + 2y = 9.60 ⇒ (1)

∵ Bag B contains 8 birthday cards and 6 thank-you notes

∵ Bag B costs $26.60

∴ 8x + 6y = 26.60 ⇒ (2)

* Lets solve this system of equations to find x and y

- Multiply equation (1) by -3 to eliminate y

∵ -3(3x) + -3(2y) = -3(9.60)

∴ -9x - 6y = -28.8 ⇒ (3)

- Add equations (2) and (3)

∴ -x = -2.2

- Multiply both sides by -1

∴ x = 2.2

∵ x represents the cost of each birthday cards

∴ The cost of each birthday card is $2.2

* Each birthday card costs $2.2

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hodyreva [135]

Answer:

C. $\frac{27}{225}=\frac{b}{100}$

Step-by-step explanation:

To find the number of black ribbons one would have subtract the amount of red ribbons from the total number of ribbons. Then one would have to express it as a proportion. Part over whole equals percent over 100. The number of black ribbons over total ribbons equals "b" over 100.

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2 years ago

Jimmy's backyard is rectangle that is 18 5/6 yards long and 10 2/5 yards wide Jim buy sod in pieces that are 1 1/3 yard long and

g100num [7]

Answer:

111 pieces of soda

Step-by-step explanation:

step 1

Find the area of the rectangular backyard

The area of the rectangular backyard is equal to

$A=LW$

where

$L=18\frac{5}{6}\ yd=\frac{18*6+5}{6}=\frac{113}{6}\ yd$

$W=10\frac{2}{5}\ yd=\frac{10*5+2}{5}=\frac{52}{5}\ yd$

substitute

$A=(\frac{113}{6})(\frac{52}{5})$

$A=\frac{5,876}{30}\ yd^2$

step 2

Find the area of one piece of sod

The area of the rectangular piece of sod is

$A=LW$

where

$L=1\frac{1}{3}\ yd=\frac{1*3+1}{3}=\frac{4}{3}\ yd$

$W=1\frac{1}{3}\ yd=\frac{1*3+1}{3}=\frac{4}{3}\ yd$

substitute

$A=(\frac{4}{3})^2\\\\A=\frac{16}{9}\ yd^2$

step 3

Find the pieces of sod needed

To find out how many whole pieces of sod will Jim need to buy to cover his backyard, divide the area of the backyard by the area of one piece of soda

so

$\frac{5,876}{30} : \frac{16}{9}=\frac{52,884}{480}=110.175$

Round up

111 pieces of soda

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yan [13]

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2 years ago

Read 2 more answers

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balandron [24]

6√90 = <span>2.11693286302546
So, this number to the power of six equals 90.
</span><span>2.11693286302546^6 = 90
</span>
The correct answer is <span>2.11693286302546. </span>

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