+280 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?
+1950 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=3.151M+1B=3.501T+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=TM=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=−7.85B=7.85/3≈$2.62
This is 262 cents or about 261 and 2/3 cents.
Thanks! :)
