+782 At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does one bagel cost?
+947
At a cafeteria,
Mary orders two pieces of toast and a bagel, which comes out to $3.15.
Gary orders a bagel and a muffin, which comes out to $3.50.
Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15.
How many cents does one bagel cost?
Mary 2T + B = 315 ............. —> T = (315 – B) / 2
Gary B + M = 350 ................—> M = (350 – B)
Larry T + 2B + 3M = 815
Substitute for Toast & Muffin into Larry's order
[(315 – B) / 2] + 2B + [3 • (350 – B)] = 815
[(315 – B) / 2] + 2B + (1050 – 3B) = 815
Multiply both sides by 2 (315 – B) + 4B + (2100 – 6B) = 1630
Combine like terms –3B + 2415 = 1630
–3B = – 785
B = 261 2/3 ¢
They usually construct these problems to come out with an even number.
I've gone back over the steps a hundred times and cannot find a mistake.
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+1365 From the problem, we can write the system
\(2T + 1B = 3.15 \\ 1M + 1B = 3.50 \\ 1T + 2B + 3M = 8.15 \)
where t is toast, b is bagel and m is muffin.
From the first two equations, we have
\( [3.15 - B ] / 2 = T \\ M = 3.50 - B\)
Subbing this in to the third equation, we have
\([ 3.15 - B ] / 2 + 2B + 3 [ 3.50 - B ] = 8.15 \\ [3.15 - B ] + 4B + 6 [ 3.50 -B ] = 16.30 \\ -3B + 3.15 + 21 = 16.30 \\ -3B = 16.30 - 3.15 - 21 \\ -3B = -7.85 \\ B = 7.85 / 3 ≈ $2.62\)
This is about 262 cents.
Thanks! :)
