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Question 364430: Sorry I have 2 very confusing questions.
question 1-
A weed spray is made of wetting agent and herbicide in the ratio 97:3 respectively. To make 20L of weed spray how much herbicide would be needed?
question 2-
The ratio of bread rolls to sandwhiches sold is 3:2 and the ratio of sandwhiches to pies sold is 4:1
a) if 15 pies are sold, how many sandwhiches where sold?
b) Using your answer to question (a) find how many bread rolls where sold.
Thank you so much to anyone who can answer these
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! First Problem:
ratio of wetting agent to herbicide is 97:3.
This means we have 97 liters of wetting agent for every 3 liters of herbicide.
Since 97 + 3 = 100, this means that our mixture will be 97% wetting agent and 3% herbicide.
We want 20 liters total.
97% of 20 = 19.4 liters.
3% of 20 = .6 liters.
That's the mix that we require./
If we are correct, then 97/3 should be the same as 19.4/.6
Our comparison equation is 97/3 = 19.4/.6.
Cross multiply to get 97*.6 = 3 * 19.4
Simplify to get:
58.2 = 58.2
The ratio are the same so we're good.
Another way of looking at is:
ratio of wetting agent to herbicide is 97/3.
If we let w = wetting agent, and h = herbicide, this means that:
w/h = 97/3
multiply both sides of this equation by h to get:
w = 97/3 * h.
we know that the weed spray is composed of w + h.
if we let s = weed spray, then the equation becomes s = w + h.
since we know that w = 97/3 * h, then the equation becomes s = 97/3*h + h.
we know that s = 20 liters, so our equation becomes 20 = 97/3*h + h
multiply both sides of this equation by 3 to get 60 = 97*h + 3h which then simplifies further to 60 = 100*h.
divide both sides of this equaqtion by 100 to get h = .6
if h = .6, then w must equal 19.4 because w + h = 20.
Same answer so we're good.
answer is that you will need 19.4 liters of wetting agent and .6 liters of herbicide.
Second Problem:
The ratio of bread rolls to sandwiches sold is 3:2 and the ratio of sandwiches to pies sold is 4:1
a) if 15 pies are sold, how many sandwiches where sold?
b) Using your answer to question (a) find how many bread rolls where sold.
Since the ratio of sandwiches to pies sold is 4:1, then if we sold 15 pies, we must have sold (4/1) * 15 = 60 sandwiches.
This is because for every 1 pie that we sell, we sell 4 sandwiches.
That's 4 times as many.
4 times 15 = 60.
Since the ratio of bread rolls to sandwiches sold is 3:2, then if we sold 60 sandwiches, we must have sold (3/2) * 60 = 90 bread rolls.
That's because for every 2 sandwiches that we sell, we sell 3 bread rolls.
Since we sold 60 sandwiches, we divide that by 2 to get 30 pairs of sandwiches and then we multiply that by 3 to get 90 bread rolls.
Bottom Line is:
We sold 90 bread rolls.
We sold 60 sandwiches.
We sold 15 pies.
ratio of bread rolls to sandwiches is 90/60 = 3/2.
ratio of sandwiches to pies is 60/15 = 4/1.
Extra:
The ratio of bread rolls to pies is (3/2) * (4/1) = (12/2) = 6/1.
90/15 = 6 which is the same as 6/1.
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