+217 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?
+1892 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! :)
