I wish you all a safe and relaxing break! (Especially those students from Mr. Milette's class who are finished their ISPs!)
POTW #23 Grade 8 Solution:
POTW #23 Grade 7 Solution:
POTW #24 Grade 7/8 Question: Happy March break!
Try it algebraically...
Grade 7/8 POTW:
ReplyDelete(yay march break)
Anyways,
Let c be the amount of concentrate in litres and w be the amount of water in litres.
c/w = 1/2
c+1/w+1 = 2/3
We can cross multiply the first one to get: w+1 = 2c, or w=2c-1
We can cross multiply the second one to get:
3(c+1) = 2(w+1)
3c+3 = 2w+2
Now we can use the first equation (2=2c+1) to substitute it into the original equation.
OK AT THIS POINT, IT’S HARDER TO SHOW ONLINE, SO I’LL DO THIS ON PAPER. IF YOU WANT TO SEE WHAT I DID, JUST ASK ME, I SHOULD HAVE IT. I’LL STILL TRY TO EXPLAIN THIS
(This is all explaining what’s happening below this giant chunk of text) So, we can use a curly bracket { and place our equations inside while also labelling each equation. Then we want to use substitution and “sub equation 2 into 1”. Then we just solve.
{ (c+1/w+1 = 2/3) ——— 1
{ (w=2c - 1) ——————2
Sub 2 into 1
(c+1/(2c-1)+1) = 2/3
c+1/ 2c = 2/3
2(2c) = 3(c+1)
4c - 3c = 3
c = 3 —— 3
Sub 3 into 2
w = 2(3) - 1
w = 6-1
w = 5
Therefore, 3 litres of concentrate and 5 litres of water will be used.
Such a thorough and clear solution! Have a great March Break Fiona.
ReplyDeleteGrade 7/8 POTW
ReplyDeleteOkay, so we know that 1 litre of water added is juice:water, 1:2, or ½. When 1 litre of juice is added, then the ratio is 2:3, or ⅔. Let x = the original amount water in litres and y = the original amount of juice in litres.
First, we know that y/(x + 1) = ½. To simplify this, we can do:
y/(x + 1) = ½
2y/(x + 1) = 2(½)
2y/(x + 1) = 1
2y/(x + 1)(x + 1) = x + 1
2y = x + 1
2y - 1 = x
We also know that (y + 1)/(x + 1) = ⅔. We can now use substitution to solve.
(y + 1)/(x + 1) = ⅔
(y + 1)/(2y - 1 + 1) = ⅔
(y + 1)/(2y) = ⅔
(y + 1)/(2y)(2y)(3) = ⅔(3)(2y)
3y + 3 = 4y
3y - 3y + 3 = 4y - 3
3 = y
Now, to find out what x =, we just need to finish a previous equation. For example 2y - 1 = x, 2(3) - 1 = x, 6 - 1 = x, 5 = x.
Therefore, the original ratio of juice to water would have been 3:5 (in litres).
POTW:
ReplyDeleteMy POTW was done on paper. Answer, 3:5.
Here's a bit of what I did:
Let j equal to juice (in litres, original mixture)
Let w equal to water (in litres, original mixture)
1:2
j / w + 1 = 1:2
When one litre of juice is added:
j + 1 / w + 1 = 2:3
From here, I found the algebraic equations and determined the original ratio of juice to water (3:5).