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?
+4 Let's assume the cost of one piece of toast is T cents, the cost of one bagel is B cents, and the cost of one muffin is M cents.
From the given information, we can create the following equations:
Equation 1: 2T + B = 315 (Mary's order)
Equation 2: B + M = 350 (Gary's order)
Equation 3: T + 2B + 3M = 815 (Larry's order)
To solve these equations, we can use a method called substitution.
From Equation 2, we can express M in terms of B: M = 350 - B
Now, let's substitute this value of M into Equation 3:
T + 2B + 3(350 - B) = 815
T + 2B + 1050 - 3B = 815
T - B = -235 ...(Equation 4)
We now have two equations with two variables: Equation 1 (2T + B = 315) and Equation 4 (T - B = -235).
Solving these equations simultaneously, we get:
2T + B = 315 ...(Equation 1)
T - B = -235 ...(Equation 4)
By adding Equation 1 and Equation 4 together, we eliminate B:
3T = 80
T = 80 / 3
Substituting the value of T back into Equation 4:
(80/3) - B = -235
B = 235 - (80/3)
Calculating the value of B:
B = 705/3
B = 235
Therefore, one bagel costs 235 cents.
I hope this answer help you to solve your question.
Thanks, James GBWA
Good work, Double-oh Seven, but with a simple mistake, I think.
You lost me at
Substituting the value of T back into Equation 4:
(80/3) - B = -235
B = 235 - (80/3)
Shouldn't this have been B = 235 + (80/3) ???????
From that we get 705 + 80
B = ——–————
3
Which is B = 785 / 3 = 261.666667
and that's the same answer that I got when I solved (tried to solve?)
this problem at https://web2.0calc.com/questions/system_86906
I thought maybe there'd been something wrong, either with the problem
or with my feeble efforts, since problems like this usually come out even.
.
