Ask question

Ask question

All categories

3 years ago

12

If you buy six pens and one mechanical pencil, it will cost $9. If you buy four pens and two mechanical pencils, it will cost $8

. How much does each pen and mechanical pencil cost?
if you let p=the cost of pen
m= the cost of mechanical pencil

6p+1m=$9
4p+2m=$8
p=? m=?
please help what do i do to find these variables? thank u

1 answer:

xeze [42]3 years ago

5 0

Use Substitution or Elimination

1. pick one equation and solve for a variable

6p + 1m = 9

1m = 9-6p

m = 9 - 6p/ 1

m= 9-6p

2. substitute m into one of the equations given

4p + 2 ( 9-6p) = 10

4p + 18 - 12p = 10

4p - 12p = 10 - 18

-8p = -8 (divide both sides by -8)

p = 1

3. Insert p=1 into any of the equations

6p+1m = 9

6(1)+1m =9

6 + 1m = 9

1m = 9-6

1m= 3

m = 3

You might be interested in

Which is the graph of the equation y-1 =

Margaret [11]

(1×3=3×1(-3,

Step-by-step explanation:

8$$_899(+¿????

7 0

3 years ago

Please help, I need this work done.

tekilochka [14]

Slope = (8 - 0)/(0 - 4) = -2
y intercept b = 8

y = mx + b where m = - 2 and b = 8
So equation y = -2x + 8

Answer
D. last one
y = -2x + 8

5 0

3 years ago

Daniela and Jack are hiking a steady incline. They use their GPS device to determine their elevation every 15 minutes. At 15 min

kow [346]

Answer:

$h=40t+9700$

where the elevation, h, is in feet and time, t, is in minutes.

Step-by-step explanation:

At the time, $t_1=15$ min, the elevation, $h_1= 10,300$ feet and

at the time $t_2= 30$ min, the elevation, $h_2=10,900$ feet.

As they are hiking a steady incline, so the change in the elevation with respect to time will be constant.

So, there will be a linear relationship between the elevation and the time.

Let $h$ be the elevation at any time instant $t$ , so the linear relation among these quantities is

$h=mt+C_0\;\cdots(i)$

where $m$ is the rate of change of elevation with respect to time and $C_0$ is constant.

The change in the elevation, $\Delta h=h_2-h_1= 10,900-10,300=600$ feet.

and the change in time, $\Delta t=t_2-1_1=30-15=15$ min.

So, change in the elevation in unit time,

$m=\frac{\Delat h}{\Delta t}=\frac{600}{15}=40$ feet/min.

Now, from equation (i)

$h=40t+C_0$

As the elevation, $h=h_1$ at time $t=t_1$ , so

$10,300=40\times15+C_0$

$\Rightarrow C_0=9700$

Hence, the required equation is

$h=40t+9700$

where the elevation, $h$ , is in feet and time, $t$ , is in minutes.

3 0

3 years ago

Lacey is putting 3902 books into boxes. She needs to put 89 books in each box. Approximately how many boxes will she need.

shepuryov [24]

Answer:

about 43 or so

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What is the scale factor of two similar pyramids with volume of 13824 cubic feel and 216 cubic feet?

velikii [3]

Answer: The scale factor is 4

Step-by-step explanation:

We know that the pyramids are similar. The volume of one of these pyramids is 13,824 cubic feet and the volume of the other one is 216 cubic feet. Then:

$V_1=13,824ft^3\\V_2=216ft^3$

By Similar solids theorem, if two similar solids have a scale factor of $\frac{a}{b}$ , then corresponding volumes have a ratio of $\frac{a^3}{b^3}$

Then:

$\frac{V_1}{V_2}=\frac{a^3}{b^3}$

Knowing this, we can find the scale factor. This is:

$\frac{13,824}{216}=\frac{a^3}{b^3}\\\\\frac{13,824}{216}=(\frac{a}{b})^3\\\\\frac{a}{b}=\sqrt[3]{\frac{13,824}{216}}\\\\scale\ factor=\frac{a}{b}=4$

3 0

3 years ago