math problems [help meee.]?

Question

1. you serve one friend 1/6 of a pie and another friend eats 1/4 of the pie. the two portions of pie contain 645 calories. how many calories are in the whole pie? how many calories are in the remaining pie ?

2. several friends go out to a buffet dinner that costs $15.95 per person. each person orders a everage that costs $1.75. the total amound of the bill is $106.20. how many friends went to dinner?

im so confused; i dont get them at all.

Answer 1

1. you serve one friend 1/6 of a pie and another friend eats 1/4 of the pie. the two portions of pie contain 645 calories. how many calories are in the whole pie? how many calories are in the remaining pie ?
1/6 + 1/4 = (2 + 3) / 12 = 5 /12
Let x denote the number of calories in the entire pie.
(5 / 12)x = 645 calories
x = (12 / 5)(645)
x = 1548 calories.
The number of calories in the remainder of the pie are
1548 - 645 = 903 calories.

2. several friends go out to a buffet dinner that costs $15.95 per person. each person orders a beverage that costs $1.75. the total amount of the bill is $106.20. how many friends went to dinner?

Per person cost: $15.95 + $1.75 = $17.70.
Total cost / individual cost =
(106.20) / (17.70) = 6.

Answer 2

1. 1/6 +1/4 = 645 calories

add the fractions, by first putting them both over 12

(1/6) (2/2) + (1/4)(3/3)

(2/2 and 3/3 are equal to 1 and so we can multiply the fractions by them without changing any values)

2/12 + 3/12 = 5/12

so 5/12 = 645

1/12 would be 645/5 or 129 calories

the whole pie is 12/12 so it's 12*129 = 1548 calories

the remaining pie is 7/12 so it's 7*129 = 903 calories

to check add the 645(eaten) + 903(remaining) to get 1548 (whole) and it works so it's right!

2. each person spent 15.95 (meal) and 1.75 (drink) = 17.70

to find out how many went out, divide total bill, by amount per person

106.20/17.70 = 6 people

Answer 3

1. (1/6)+(1/4) = (4/24)+(6/24) = 10/24 = 5/12

5 parts => 645 calories
12 parts => (645/5)*12 = 1548 calories

2. Cost per person = 15.95+1.75 = 17.70
Number of friends = 106.20/17.70 = 6 friends

Answer 4

1/6+1/4 = 5/12 of pie = 645 clories
So whole pie has (12/5)(645) = 1548 calories
1548-645 = 903 calories left in pie.

15.95 + 1.75 = $17.70 per person
106.20/17.70 = 6 persons

Answer 5

ok, so...
you have to make the 1/6 and 1/4 into numbers with a common denominator...
so change 1/6 to an equivalent like 2/12 (multiply top and bottom by 2) and change 1/4 to 3/12 (multiply top and bottom by 3) and now you have to fractions witha common denominator... add them together and you get 5/12. If these two portions together contain 645 calories then what you have to do is divide by 5 to get the amount of calories per 1/12 and then multiply by 12. if you do this you get 1548 calories for the whole pie.

ok so for the second question you have to add the price of the dinner and the beverage together to see what each person spent. you get $17.70. now divide $106.20 by $17.70 to see how many people went to dinner. you get 6 people.

hope that helps!

Answer 6

1. Imagine the pie being cut up into 12 pieces. So,

1/6x+1/4x=645
2/12x+3/12x=645
5/12x=645
5x=7,740
x=1,548

The total amount of calories in the pie is 1,548 calories.
The calories in the remaining pie are 7/12 of the full pie, which is 903 calories, or you can just subtract 1,548-645=903 calories.

2. 15.95x+1.75y=106.20 (x is the amount of food ordered and y is the amount of drinks ordered.) Since the amount of food = the amount of drinks, then x=y.

17.70x=106.20
x=6
y=6
6 meals, 6 drinks, 6 people.