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Will and Grace are canoeing on a lake.  Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. If they always row directly towards each other, and the lake is $2800$ meters across from the west side of the lake to the east side, at what time will the two meet?

 

The system of equations

xy/(x + y) = 2 xz/(x + z) = 2 yz/(y + z) = 2
has exactly one solution. What is  in this solution?

 

I have to paint one side of a wall.  The wall is $6$ meters tall and $60$ meters long.  Each gallon of paint covers $200$ square feet.

 

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to . Gary orders a bagel and two muffins, which comes out to . Larry orders a piece of toast, two bagels, and a muffin, which comes out to . How many cents does one bagel cost?

 

In Linguistics  the ratio of the number of juniors to the number of seniors is . When  more juniors join the class, and  senior drops the class, the ratio of the number of juniors to the number of seniors becomes . How many students are in the class after these changes?

 Oct 25, 2024
 #1
avatar+1926 
+1
 Oct 26, 2024
edited by NotThatSmart  Oct 26, 2024
 #2
avatar+1926 
+1

3. 

Let's set up a system of equations to solve this problem. 

Let's let b be bagels

Let's let t be toast

And let's let m be muffins. 

 

From the problem, we have the system

\(2T + 1B = 3.15 \\ 1M + 1B = 3.50 \\ 1T + 2B + 3M = 8.15\)

 

Now, we want everything to be in terms of bagels. 

From the first two equations, we get the equations

\([3.15 - B ] / 2 = T \\ M = 3.50 - B\)

 

Now, plugging these values into the third equation, we get

\([ 3.15 - B ] / 2 + 2B + 3 [ 3.50 - B ] = 8.15 \\ [3.15 - B ] + 4B + 6 [ 3.50 -B ] = 16.30 \\ -3B + 3.15 + 21 = 16.30 \\ -3B = 16.30 - 3.15 - 21 \\ -3B = -7.85 \\ B = 7.85 / 3 ≈ $2.62\)

 

This is 262 cents or about 261 and 2/3 cents. 

 

Thanks! :)

 Oct 26, 2024
edited by NotThatSmart  Oct 26, 2024

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