can you please answer theses problems please. 1st, find three consecutive odd integers such that the same of the smallest and 4 times the largest is 61 . next juan is 8 years older than his sister in 3 year he will be twice as old as she will be the how old are they now. next, c and y candy company mixes candy that cost $6.00 per kg with candy that costs $ 4.50 per kg how many killograms of each are needed to make a 3kg bag that cost $15.00 last problem im sorry im asking for much but its for a test and if i pass it i move onto geometry. how much water must be added to a 12 grams of a 90% iodine solution to produce a 25% iodine solution. thanks if you can anser that will be great if this is too much plz leave your answers but showing work will help me more
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1)
Consider 3 odd integers to be 2n+1, 2n+3, 2n+5
sum of the smallest and 4 times largest is 61 so, smallest is 2n+1 largest is 2n+5
hence, 2n+1+4(2n+5)=61
this gives, 2n+1+8n+20=61
thus 10n=61-1-20
10n=40
n=4
so consecutive numbers are:
(2*4)+1=9
(2*4)=3=11
(2*4)+5=13
2)
let juan's present age be X and sister's present age be Y
juan is 8 years older than sister, so X=Y+8------------ equation 1
in three years he will be twice as old as her, so u get the equation
X+2 = 2(Y+2)---------------equation 2
substituting equation 1 in equation 2 we get.....
Y+10=2Y+4
thus Y=6
substituting Y in equation 1 we get... X=14
3)
Let weight for $6.00 candy be X
let weight for $4.50 candy be Y
now total cost is equal to their weights * induvidual cost!!
ie, cost incurred due to $6.00 per kg candy is 6*X
cost incurred due to $4.50 per kg candy is 4.5*Y
so total cost is $15 hence
6*X + 4.5*Y=15
total weight is 3Kg
so X+Y=3
6X+4.5Y=15
X+Y=3
solving we get
X=1 and Y=2 ie weight of $6.00 is 1 and other weight is 2Kg
4)
12 gms of 90%iodine solution will have:
12*90/100 =10.8 gmsof iodine
Consider 3 odd integers to be 2n+1, 2n+3, 2n+5
sum of the smallest and 4 times largest is 61 so, smallest is 2n+1 largest is 2n+5
hence, 2n+1+4(2n+5)=61
this gives, 2n+1+8n+20=61
thus 10n=61-1-20
10n=40
n=4
so consecutive numbers are:
(2*4)+1=9
(2*4)=3=11
(2*4)+5=13
2)
let juan's present age be X and sister's present age be Y
juan is 8 years older than sister, so X=Y+8------------ equation 1
in three years he will be twice as old as her, so u get the equation
X+2 = 2(Y+2)---------------equation 2
substituting equation 1 in equation 2 we get.....
Y+10=2Y+4
thus Y=6
substituting Y in equation 1 we get... X=14
3)
Let weight for $6.00 candy be X
let weight for $4.50 candy be Y
now total cost is equal to their weights * induvidual cost!!
ie, cost incurred due to $6.00 per kg candy is 6*X
cost incurred due to $4.50 per kg candy is 4.5*Y
so total cost is $15 hence
6*X + 4.5*Y=15
total weight is 3Kg
so X+Y=3
6X+4.5Y=15
X+Y=3
solving we get
X=1 and Y=2 ie weight of $6.00 is 1 and other weight is 2Kg
4)
12 gms of 90%iodine solution will have:
12*90/100 =10.8 gmsof iodine
12
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