Question 1146718: A hummingbird needs 10 grams of sugar and 8 grams of protein each day. One honeysuckle flower provides 20 mg of sugar and 10 mg of protein. One nasturtium flower provides 10 mg of sugar and 10 mg of protein. It takes 5 seconds to feed from a nasturtium and 5 seconds per honeysuckle. How many minutes does it take to get exactly the food it needs? (1 gram equals 1000 mg.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you would probably want to make a table as shown below.
before doing that, translate everything to milligrams.
10 grams = 10,000 milligrams
8 grams = 8,000 milligrams.
you could also have converted everything to grams.
either way should get you the same answer.
let x = the number of honeysuckle flowers.
let y = the number of nasturtium flowers.
your table would look like this:
honeysuckle flowers nasturtium flowers total
number of x y
mg of sugar 20 10 10,000
mg of protein 10 10 8,000
your equations would be:
20 * x + 10 * y = 10,000
10 * x + 10 * y = 8,000
subtract the second equation from the first to get:
10 * x = 2,000
solve for x to get:
x = 200
replace x with that in the first equation and solve for y to get:
20 * 200 + 10 * y = 10,000
simplify to get:
4,000 + 10 * y = 10,000
subtract 4,000 from both sides to get:
10 * y = 6,000
solve for y to get:
y = 600
you have:
x = 200
y = 600
replace x and y with that in both original equations to get:
20 * x + 10 * y = 10,000 becomes 20 * 200 + 10 * 600 = 10,000 which becomes 4000 + 6000 = 10,000 which becomes 10,000 = 10,000 which is true.
10 * x + 10 * y = 8,000 becomes 10 * 200 + 10 * 600 = 8,000 which becomes 2000 + 6000 = 8,000 which becomes 8,000 = 8,000 which is true.
the number of each type of flower looks good.
it takes 5 seconds to feed from each flower.
(200 + 600) * 5 = 800 * 5 = 4000 seconds.
4000 seconds / 60 seconds per minute = 66 and 2/3 minutes.
that's how long it takes the hummingbird to get exactly the amount of sugar and protein that it needs.
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