Question 1100352: An average bagel contains 30 mg of calcium and 2 mg of iron. One ounce of cream cheese contains 25 mg of calcium and 0.4 mg of iron. If Leyla wants to eat a combination of bagels and cream cheese that contains exactly 370 mg of calcium and 12 mg of iron, how much of each should she eat?
How many bagels does she need to eat?
How many ounces of cream cheese does she need?
Found 2 solutions by richwmiller, jim_thompson5910:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 1) 30b+25c=370
2) 2b+.4c=12
Let's solve by elimination.
multiply equation 2 by 15
30b+.4*15*c=12*15
simplify
3) 30b+6c=180
subtract 3) from 1)
30b+25c=370
30b+6c=180
solve for c
19c=370-180
19c=190
c=10 oz cream cheese
substitute c into equation 2)
2b+.4*10=12
2b+4=12
2b=8
b=4 bagels
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website!
Let,
x = number of bagels she needs to eat (this is a positive whole number)
y = amount, in ounces, of cream cheese she needs to eat (this is some positive number which could be a whole number or a decimal number)
"An average bagel contains 30 mg of calcium" and "One ounce of cream cheese contains 25 mg of calcium". So if Leyla eats x bagels and y ounces of cream cheese, then she'll consume 30x+25y mg of calcium in total. She needs 370 mg of calcium meaning that the first equation is 30x+25y = 370
The second equation is 2x+0.4y = 12 because
she gets 2 mg of iron from each bagel, so 2*x mg of iron from all the bagels she eats
she also gets 0.4 mg of iron per ounce of cream cheese, giving another sub-total of 0.4*y mg of iron
Overall she consumes 2x+0.4y mg of iron. This amount must be equal to 12 as this is the target value for iron.
The two equations in this system are
30x+25y = 370
2x+0.4y = 12
Let's solve the second equation for x
2x+0.4y = 12
2x+0.4y-0.4y = 12-0.4y subtract 0.4y from both sides
2x = 12-0.4y
2x/2 = (12-0.4y)/2 divide both sides by 2 to isolate x
x = (12/2)-(0.4y/2)
x = 6-0.2y
Then plug this into the first equation
30x+25y = 370
30*(x)+25y = 370
30*(6-0.2y)+25y = 370 x has been replaced with 6-0.2y
Next we isolate y
30*(6-0.2y)+25y = 370
30*(6)+30*(-0.2y)+25y = 370 distribute
180-6y+25y = 370
180+19y = 370
180+19y-180 = 370-180 subtract 180 from both sides
19y = 190
19y/19 = 190/19 divide both sides by 19 to get y all by itself
y = 10
Use this value of y to find x
x = 6-0.2y
x = 6-0.2*10 replace y with 10
x = 6-2
x = 4
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In summary we get
x = 4
y = 10
Recall that at the top of the problem, we let,
x = number of bagels she needs to eat
y = amount, in ounces, of cream cheese she needs to eat
So Leyla needs to eat 4 bagels and 10 ounces of cream cheese to reach her goal (of consuming exactly 370 mg of calcium and 12 mg of iron)
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