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?
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?
Looks like a substitution problem. Let's see what we've got.
Mary's order: 2T + B = 3.15
Gary's order: B + M = 3.50
Larry's order: T + 2B + 3M = 8.15
per Mary's 2T + B = 3.15
2T = 3.15 – B
T = (3.15 – B) / 2
per Gary's B + M = 3.50
M = 3.50 – B
Now we have the toast and the
muffin in terms of the bagel, so
substitute into Larry's order T + 2B + 3M = 8.15
[(3.15 – B) / 2] + 2B + (3)(3.50 – B) = 8.15
Multiply everything by 2, to get
rid of that denominator (3.15 – B) + 4B + (6)(3.50 – B) = 16.30
Now it's just a question of
multiplying and adding; it's
tedious, but simple. 3.15 – B + 4B + 21.00 – 6B = 16.30
24.15 – 3B = 16.30
– 3B = 16.30 – 24.15
– 3B = – 7.85
Usually, the problems like this are B = 2.61667 dollars
crafted to come out even. I have
gone over this thing, I don't know, B = 262 ¢
probably 20 times and I can not
find a mistake. I would gratefully
appreciate it, if some one spots
a mistake, post a comment telling
me where I messed up. Thanks.
.
