For the math lovers, can you help me?

1. The length of a rectangular yard is 3 yards more than twice the width. The perimeter is 72 yards. What is tfhe width of the yard?


a) 11yd


b) 11.5 yd


c) 12 yd


d) 13 yd





2. Grace is buying peanuts and raisins to make a snack mix for her coworkers at an office meeting. She will buy peanuts for $5.50 per pound and raisins for $4 per pound. How many pounds of raisins shouls she buy to make 10 pounds of the snack mix that is worth $4.90 per pound?


a) 3 lb


b) 4 lb


c) 5 lb


d) 6 lb





3. Kennedy purchased 4 different kinds of apples: Jonathon, Red Delicious, Yellow Delicious, and MacIntosh. She bought twice as many MacIntosh as Jonathon and twice as many Jonathon as Red Delicious. The number of Red Delicious apples is the same as the number of Yellow Delicious apples. If she places all of the apples in a basket and chooses one apples at random, what is the probability that she chooses a Jonathon apple?


a) 0.2


b) 0.25


c) 0.4


d) 0.5

For the math lovers, can you help me?
Hi, Jackie. I'll give it a shot.


1. The length of a rectangular yard is 3 yards more than twice the width. The perimeter is 72 yards. What is the width of the yard?


Let x = the width of the yard


then, 2x + 3 is the length of the yard.


P = 2l + 2w; so,


72 = 2(2x + 3) + 2x


72 = 4x + 6 + 2x


72 = 6x + 6


66 = 6x


11 = x, the width


a) 11yd ☺


b) 11.5 yd


c) 12 yd


d) 13 yd





2. Grace is buying peanuts and raisins to make a snack mix for her coworkers at an office meeting. She will buy peanuts for $5.50 per pound and raisins for $4 per pound. How many pounds of raisins shouls she buy to make 10 pounds of the snack mix that is worth $4.90 per pound?





Let x = the number of pounds of peanuts


Then, 10 - x is the # of pounds of raisins


5.50x + 4(10 - x) = 4.90(10)


5.50x + 40 - 4x = 49


1.50 x + 40 = 49


1.5x = 9


x = 6


So, 6 pounds of peanuts and 4 pounds of raisins to give you a total of 10 pounds mixture.





a) 3 lb


b) 4 lb ☺


c) 5 lb


d) 6 lb





3. Kennedy purchased 4 different kinds of apples: Jonathon, Red Delicious, Yellow Delicious, and MacIntosh. She bought twice as many MacIntosh as Jonathon and twice as many Jonathon as Red Delicious. The number of Red Delicious apples is the same as the number of Yellow Delicious apples. If she places all of the apples in a basket and chooses one apples at random, what is the probability that she chooses a Jonathon apple?





Let x = # of red delicious


then x = # of yellow delicious


and 2x = # of jonathans


and 2(2x) = 4x is the number of MacIntosh


if she bought 1 red, 1 yellow, 2 jonathans and 4 macIntosh (totaling 8 apples) then 2 of the 8 will be Jonathans. 2/8 = 1/4 = .25


Note whatever you choose for x; 1, 2, 3...etc the same ratio will come along everytime...1/4 or .25.


a) 0.2


b) 0.25☺


c) 0.4


d) 0.5
Reply:1)


(3+2x+x)*2=72


3+3x=36


3x=33


x=11


2)


4,9=(5,5*(10-x)+4*x)/10


49=5,5*(10-x)+4x


49=55-5,5x+4x


-6=-1,5x


x=4


3)


Red Delicious=x


yellow delicious =x


Jonathon = 2x


Maclntosh = 4x


together = 8x


jonathon is 2 out of 8 or 1/4 or 0,25
Reply:In all cases, write down what you know, set up the equations, then solve them.





For example, in number 1: let the length be l, and the width w.





We are told that l = 3 + 2w


We are told that 2l + 2w = 72





Substitute the first equation in to the second, solve for w, then solve for l.





You're done!





The other problems are similar.
Reply:c a d
Reply:1)


width = W


length = L = 2W + 3


Perimeter = 2W + 2L = 72





2W + 2(2W + 3) = 72


2W + 4W + 6 = 72


6W = 66


W = 11 yds





2)


Peanuts: 5.50 dollars / pound


Raisins: 4.00 dolalrs / pound





x pounds of peanuts plus y pounds of raisins = 10 pounds of snack mix....


x + y = 10





If she buys 10 pounds of snack mix, her total cost is:





10 pounds * 4.90 dollars / pound = 49 dollars





[5.50 dollars / pound] * x pounds + [4.00 dollars / pound] * y pounds


=


5.50x dollars + 4.00y dollars = 49 dollars


or


5.5x + 4y = 49





But from above, x + y = 10





so solve the system of equations:


5.5x + 4y = 49


x + y = 10








5.5x + 4y = 49


-4(x + y = 10) ---%26gt; -4x - 4y = -40





5.5x + 4y = 49


-4x - 4y = -40





1.5x + 0 = 9


x = 6 pounds


y = 4 pounds





raisins were "y", so y = 4 pounds








3)


Macintosh = M


Jonathon = J


Red Delicious = R


Yellow Delicious = Y





Translate the paragraph:





M = 2J


J = 2R


R = Y





Since R = Y, J = 2Y


since J = 2Y, M = 4Y





So,


M = 4Y


J = 2Y


R = Y


Y = Y





Total # apples = M + J + R + Y


= 4Y + 2Y + Y + Y = 8Y





Probability(Chooses a jonathon) = # Jonathons / # Total Apples





=


2Y / 8Y = 1/4