Powder Nos
Powder Nos
A vase contains 90 kgs.of powdered milk and 10 kgs. of sugar. How much sugar must be added to make 25% sweet?
1.In making brass, the metals copper and zinc are to be mixed in the proportion of 4 parts of copper to 6 parts of zinc, by weight. how many kilograms of each are required to make 8 metric tons of brass?
2. How many kilogram of fine glucose must be added to 25 kilograms of a 12% sweetened juice concentrate to prepare instead a light syrup 20% sweet?
3. The square of the first number, exceeds the second number by 11. The square of the difference between the second number and the first is 361. Find the numbers.
4. The sum of the squares of the reciprocals of 2 nos. is 5/64. If 3 times the reciprocal of the 1st no. if added to 2 times the 2nd no., the result is the same as the product of the 1st no. and it reciprocal. Find the numbers.
5. Find two consecutive even numbers whose product is 360.
6. Find 2 consecutive positive integers whose product is 240.
ok so for your title question. you want 25% sweet as in 25% sugar and you have 90kg milk. so the milk will be 75% of the mixture. so you do a like milk/75% = total/100% and solve for total. so you get a number (120) which is the total mixture. then subtract 90 from it to get the amount of sugar. which is 30, but you already have 10 so you have ot add 20 more.
number 1. so the mixture is 40% copper and 60% zinc, by weight. so out of 8 metric tons whcih is 8000 kg. you find how much 40% of it is (3200kg) and then how much 60% is (4800kg) by multiplying 8000 x 40% or 8000 x 0.40 and then same with 60.
number 2. so in this case, out of 25kg, 12% is sweet stuff (glucose). so you find out what 12% of 25kg is by doing 25 x 0.12 = 3. so 3 kg is glucose. and you have to add glucose until its 20% sweet. so the 25kg - 3kg is the other stuff in the mixture (not including the glucose) which is 22kg. and that 22kg stays at 22kg and it makes up 80% of the new mixture. so you do the whole 22/80% = total/100%. so thats 27.5kg. so you have to add glucose until its 27.5kg. and you have 25 now so you have to add 2.5kg of glucose.
number 3. this is algebra. write down equations for each and make up variables.
so first eq. a^2 = b+11
second. (b-a)^2 = 361
then you solve the two equations. this is kinda hard though. since a^2 = b+11, b = a^2-11 and put that in the other eq and you get a^2 - a - 11 = sqrt 361 = 19
so then you get a quadratic equation a^2 - a - 30 = 0
this is easy its just (a-6)(a+5) (since -6 and 5 add to -1 and multiply to -30). so a is either 6 or -5. you try both of them in your two equations to see if any work.
so with a=6. b-6 = 19. b = 25. so then and this one works. 6^2 = 36 = 25+11
then try a=-5 b+5=19. b=14. a^2 = 25 = b+11 so they both work.
and now 4. u know u should do your own homework. im tired. i so better get best answer for this.
so sum of squares of reciprocals. wow confusing. so ok the first number is a/b. and the 2nd number is c/d.
eq 1. (b/a)^2 + (d/c)^2 = 5/64
eq 2. 3 (b/a) + 2(d/c) = (b/a)(a/b) = 1
so you can put a e=b/a cuz why not. and f=d/c
e^2 + f^2 = 5/64
3e + 2f = 1 so 2f = 1-3e and so f = (1-3e)/2
so then e^2 + (1-3e)^2/4 = 5/64
e^2 + (1 - 6e + 9e^2) = 5/16
10e^2 - 6e + 1 = 5/16 multiply by 16
160e^2 - 96e + 16 = 5
160e^2 - 96e + 11 = 0 so use quadratic equation
e = something. put it in. you know what to do
5. so you can use 2 consecutive even numbers. the way i would do it is just go through and multiply and check. like 12*14 then 14*16 16*18 etc. its 18 and 20 btw. if you have to solve it then you would get 2 equations
a = b+2
ab = 360
(b+2)b = 360 b^2 + 2b - 360 = 0 so quadratic equation
6. so same thing basically. but this time when you use the quadratic, you cant use the negative number so you only have 1 solution. and the numbers end up being 15 and 16.
post questions u have, ill try to come back and help
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