Ask question

Ask question

All categories

3 years ago

7

Jessica ordered 10 bouquets of tulips, 4 bouquets of roses, and 6 bouquets of lilies for a total of $670. The combined cost to b

uy one of each type of bouquet is $115. If a bouquet of lilies costs $5 more than a bouquet of tulips, what is the cost of each type of flower bouquet? A. The cost of one bouquet of tulips is $30, one bouquet of roses is $60, and one bouquet of lilies is $25. B. The cost of one bouquet of tulips is $25, one bouquet of roses is $30, and one bouquet of lilies is $60. C. The cost of one bouquet of tulips is $25, one bouquet of roses is $60, and one bouquet of lilies is $30. D. The cost of one bouquet of tulips is $26, one bouquet of roses is $60, and one bouquet of lilies is $31.

1 answer:

LUCKY_DIMON [66]3 years ago

8 0

Answer:C

Step-by-step explanation:

Let x represent the cost of a bouquet of tulips.

Let y represent the cost of a bouquet of roses.

Let z represent the cost of a bouquet of lilies.

Jessica ordered 10 bouquets of tulips, 4 bouquets of roses, and 6 bouquets of lilies for a total of $670. This means that

10x + 4y + 6z = 670 - - - - - - - - - 1

The combined cost to buy one of each type of bouquet is $115. This means that

x + y + z = 115- - - - - - - - - 2

If a bouquet of lilies costs $5 more than a bouquet of tulips, it means that

z = x + 5 - - - - - - - - - 3

Substituting equation 3 into equation 1 and equation 2, it becomes

10x + 4y + 6(x+5)= 670

10x +4y + 6x + 30 = 670

16x + 4y = 670 - 30

16x + 4y = 640 = - - - - - - - - - 4

Substituting equation 3 into equation 2, it becomes

x + y + x + 5 =

2x + y = 115 - 5

2x + y = 110 - - - - - - - - - 5

Multiplying equation 5 by 4 , it becomes

8x + 4y = 440 - - - - - - - - - 6

Subtracting equation 6 from equation 4, it becomes

8x = 200

x = 200/8 = 25

2x + y = 110

2×25 + y = 110

50 + y = 110

y = 110 - 50 = 60

z = x + 5

z = 25 + 5 = 30

The cost of one bouquet of tulips is $25, one bouquet of roses is $60, and one bouquet of lilies is $30.

You might be interested in

Please answer I will give BRAINLIEST if i can

N76 [4]

Answer:

Glass A holds the most, It holds more than glass B because of its cone shape.

Step-by-step explanation:

I hope I helped you, now have a good day and good luck!! ;)

7 0

3 years ago

Sindrei [870]

First you need to multiply the one in the bracket 7x2 which is 14 then u must multiply it with 3 to get the answer so 14x3 which equals to 42

7 0

1 year ago

Please help this is pre algebra :)

larisa [96]

Step-by-step explanation:

the explanaition of the answer and solution is in the picture, check it out. this is for question 14

3 0

3 years ago

1 At the post office 55% of the packages ship as priority mail. If 160 packages are

ziro4ka [17]

Answer:

72

Step-by-step explanation:

45% did not get shiped so 160*.45=72

6 0

3 years ago

The following results come from two independent random samples taken of two populations.

photoshop1234 [79]

Answer:

$(a)\ \bar x_1 - \bar x_2 = 2.0$

$(b)\ CI =(1.0542,2.9458)$

$(c)\ CI = (0.8730,2.1270)$

Step-by-step explanation:

Given

$n_1 = 60$ $n_2 = 35$

$\bar x_1 = 13.6$ $\bar x_2 = 11.6$

$\sigma_1 = 2.1$ $\sigma_2 = 3$

Solving (a): Point estimate of difference of mean

This is calculated as: $\bar x_1 - \bar x_2$

$\bar x_1 - \bar x_2 = 13.6 - 11.6$

$\bar x_1 - \bar x_2 = 2.0$

Solving (b): 90% confidence interval

We have:

$c = 90\%$

$c = 0.90$

Confidence level is: $1 - \alpha$

$1 - \alpha = c$

$1 - \alpha = 0.90$

$\alpha = 0.10$

Calculate $z_{\alpha/2}$

$z_{\alpha/2} = z_{0.10/2}$

$z_{\alpha/2} = z_{0.05}$

The z score is:

$z_{\alpha/2} = z_{0.05} =1.645$

The endpoints of the confidence level is:

$(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

$2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}$

$2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}$

$2.0 \± 1.645 * \sqrt{0.0735+0.2571}$

$2.0 \± 1.645 * \sqrt{0.3306}$

$2.0 \± 0.9458$

Split

$(2.0 - 0.9458) \to (2.0 + 0.9458)$

$(1.0542) \to (2.9458)$

Hence, the 90% confidence interval is:

$CI =(1.0542,2.9458)$

Solving (c): 95% confidence interval

We have:

$c = 95\%$

$c = 0.95$

Confidence level is: $1 - \alpha$

$1 - \alpha = c$

$1 - \alpha = 0.95$

$\alpha = 0.05$

Calculate $z_{\alpha/2}$

$z_{\alpha/2} = z_{0.05/2}$

$z_{\alpha/2} = z_{0.025}$

The z score is:

$z_{\alpha/2} = z_{0.025} =1.96$

The endpoints of the confidence level is:

$(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

$2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}$

$2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}$

$2.0 \± 1.96 * \sqrt{0.0735+0.2571}$

$2.0 \± 1.96* \sqrt{0.3306}$

$2.0 \± 1.1270$

Split

$(2.0 - 1.1270) \to (2.0 + 1.1270)$

$(0.8730) \to (2.1270)$

Hence, the 95% confidence interval is:

$CI = (0.8730,2.1270)$

8 0

3 years ago