Post # 1

Member

9917 posts

Buzzing Beekeeper

I tutor an eighth grader (usually in reading and history), but he has a big Algebra test coming up and we are trying to do this problem…I know there is an algebraic way to figure out the answer, but I can’t remember. Can you help??

13. Samantha!and!Maria!purchased!flowers.!!Samantha!purchased!5!roses!for!x!

dollars!each!and!4!daisies!for!y!dollars!each!and!spent!$32!on!the!flowers.!!

Maria!purchased!1!rose!for!x!dollars!and!6!daisies!for!y!dollars!each!and!

spent!$22.!!The!system!of!equations!below!represents!this!situation.

5x + 4y = 32

x + 6y = 22

Which!statement!is!true?

!!!!!a.!!A!rose!costs!$1!more!than!a!daisy.

b.!!Samantha!spent!$4!on!each!daisy.

c.!!Samantha!spent!more!on!daisies!than!she!did!on!roses.

d.!!Samantha!spent!over!4!times!as!much!on!daisies!as!she!did!on!roses.

Post # 5

Member

524 posts

Busy bee

- Wedding: March 2013 - Callanwolde Fine Arts Center

First you need to determine what the values of x and y are.

x+6y=22 therefore x=22-6y

Plug that back into the first equation: 5(22-6y)+4y=32

Solve for y:

110-30y+4y=32

110-26y=32

78=26y

3=y (daisys)

Use y to solve for x: x=4. (roses)

Check your work using the other equation. The answer is then A

Post # 6

Member

9917 posts

Buzzing Beekeeper

@mrshunnybunches: Ahhh I had that but then I put =32 for the second equation. D’oh this is why I am bad at math!! Thank you!

Post # 7

Member

527 posts

Busy bee

You wanted to know the process. Here it is:

You have two equations:

5x+4y=32

x+6y=22

We now know that x=22-6y.

Substitute that in with your first equation:

5(22-6y)+4y=32

110-30y+4y=32

110-26y=32

110-110-26y=32-110

-26y=-78

y=3

Post # 9

Member

9917 posts

Buzzing Beekeeper

Here is another one!! I don’t even know what equation to write. I thought the Pythagorean Theorem would work, but that gives the answer 7.2…

A ball rolls down a ramp with a slope of 2/3. At one point the ball is 10 feet high, and at another point the ball is 4 feet high, as shown in the diagram below.

[Insert right looking triangle here]

What is the horizontal distance [x], in feet, the ball traveled as it rolled down the ramp from 10 feet high to 4 feet high?

a. 6

b. 9

c. 14

d. 15

Edited for clarity, sorry about that! We’re going to work on this one on Wednesday…boy I feel dumb.

Post # 10

Member

527 posts

Busy bee

@peachacid: OK, I’m not 100% on this one. I googled the math problem to find the diagram, since I think this is actually really important.

We know the slope is 2/3. That means on a graph, it will be 2 up and 3 over. If the height of 2 points is 6 feet, then the length between each point must be 3 feet. So if the length the ball rolled is three points, the length must be 9 feet.

Sorry – I wasn’t great at graphing and using slope to solve problems!! I’m fairly sure that this is the right answer, but I’m sure there is a better way to find it!!

Post # 11

Member

2705 posts

Sugar bee

@peachacid: For the rolling ball problem, you’re going to want to use the equation for a line:

y = mx + b where m is the slope of the line (2/3) and b is where the line intersects the y-axis.

We will assume that b = 0 since it really doesn’t matter where exactly the line intersects the y-axis. We are looking for a delta/change and not specific coordinates. Does that make sense?

So now you have a lovely equation of:

y = (2/3)*x

You know y at 2 points (10 and 4) and now you just need to find the x location for those 2 points (x1 and x2).

10 = (2/3) * x1 and 4 = (2/3) * x2

x1 = 15 x2 = 6

To figure out how far the ball has rolled horizontally along the x, you just find the difference between x1 and x2.

x1 – x2 = 9. So the answer is b.

You don’t need to draw the graph, but it might also be beneficial to draw it out as mrshunnybunches did just to get a visual. However, you don’t want to rely on plotting alone. It works nicely in this problem, but it won’t always.

Post # 12

Member

527 posts

Busy bee

@RunsWithBears: I totally knew there was a better way to do this!! ðŸ˜‰