+972 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?
+1424
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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+1950 From the problem, we can write the system
2T+1B=3.151M+1B=3.501T+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=TM=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=−7.85B=7.85/3≈$2.62
This is about 262 cents.
Thanks! :)
