Mathematics, 13.11.2019 19:31, brody5453

Jane’s buying clothes. she can get 5 shirts & 4 sweaters for $229 or she can get 2 shirts & 3 sweaters for $128. how much is 1 shirt, and how much is 1 sweater?

Answers: 2

Show answers

Answers

answered: bluenblonderw

Cost of 1 shirt is $\$25$ and cost of one sweater is $\$26$

Solution:

Given that Jane’s buying clothes.

She can get 5 shirts & 4 sweaters for $\$229$

She can get 2 shirts & 3 sweaters for $\$128$

Need to determine cost of 1 shirt and 1 sweater.

Let assume cost of 1 shirt = $\$x$

And assume cost of 1 sweater = $\$y$

Let us create equations from give conditions

First condition is Cost of 5 shirt + cost of 4 sweater = $\$229$

$\begin{array}{l}{\text { cost of 5 shirts }=5 \times \text { cost of 1 shirt }=5 \times x=5 x} \\\\ {\text { cost of 4 sweater }=4 \times \text { cost of 1 sweater }=4 \times y=4 y}\end{array}$

So using first condition equation which we get is as follows

$5 x+4 y=229 \rightarrow (1)$

Second condition is Cost of 5 shirt + cost of 4 sweater = $\$128$

$\begin{array}{c}{\text { cost of } 2 \text { shirts }=2 \times \text { cost of } 1 \text { shirt }=2 \times x=2 x} \\\\ {\text { cost of } 3 \text { sweater }=3 \times \text { cost of } 1 \text { sweater }=3 \times y=3 y}\end{array}$

So using second condition equation which we get is as follows

$2 \mathrm{x}+3 \mathrm{y}=128\quad\rightarrow (2)$

Now we have two equations to be solved

$\begin{array}{l}{5 x+4 y=229 \rightarrow (1)} \\\\ {2 x+3 y=128 \rightarrow (2)}\end{array}$

On multiplying equation (1) by 2 and equation (2) by 5 to make coefficients of x equal in both equations, we get

$\begin{array}{l}{2 x(5 x+4 y)=2\times 229} \\\\ {10 x+8 y=458 \rightarrow (3)} \\\\ {5 x(2 x+3 y)=5 \times 128} \\\\ {10 x+15 y=640 \rightarrow (4)}\end{array}$

On subtracting (3) from (4), we get

$\begin{array}{l}{(10 \mathrm{x}-10 \mathrm{x})+(15 \mathrm{y}-8 \mathrm{y})=640-458} \\\\ {\Rightarrow 7 \mathrm{y}=182} \\\\ {\Rightarrow \mathrm{y}=\frac{182}{7}=26}\end{array}$

On substituting y = 26 in equation (1) we get

$\begin{array}{l}{\Rightarrow 5 \mathrm{x}+(4 \times 26)=229} \\\\ {\Rightarrow 5 \mathrm{x}=229-104} \\\\ {\Rightarrow 5 \mathrm{x}=125} \\\\ {\Rightarrow \mathrm{x}=\frac{125}{5}=25}\end{array}$

Cost of 1 shirt = $\$x = \$25$

Cost of 1 sweater = $\$y = \$26$

answered: Guest

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

$y\propto x$

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

answered: Guest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

ask for details followreport by buttfacelily 2 minutes ago

answers

rauschg

rauschg · hand

know the answer? add it here!

step-by-step explanation: