Basic math word problems?

Question

Hey, my teacher gave us a extra credit halloween themed worksheet and I desperately need the points but I'm to stupid to figure these out. Any help is awesome. Some work is necessary is but don't worry about showing every little step. Thanks!
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1. How many pounds of candy selling for $2.25 a pound should be added to two pounds of candy selling for $3.75 a pound to create a blend, which will sell for $2.85 a pound?

2. Alexis bought 14 bags of candy at the store for a total price of $41.52. She bought some bags of candy that cost $3.21 each and the rest cost $2.64 each. How many bags of the $3.21 candy did Alexis buy?

3. Austin, Anthony, and Brittany went trick or treating on halloween,. Altogether, the three of them collected 57 pieces of candy. Anthony collected 4 more than 3 times the number of pieces of candy collected by Austin. Brittany collected 7 less than the number of pieces collected by Austin. How much candy did Austin collect?

4. A bat was flying 6 hours at an average speed of 8km per hour. The bat flew at 6km per hour during the first 2 hours of its flight. How fast did the bat fly the last 4 hours?

Answer 1

[09]
1.Let x pounds of candy @$2.25 be added to 2 pounds of candy@3.75 to make x+2 pounds of candy selling at $2.85
By the problem,
2.25x+2*3.75=2.85(x+2)
2.25x+7.50=2.85x+5.70
2.25x-2.85x=5.70-7.50
-0.60x= -1.80
x= -1.80/-0.6=3
Ans. 3 pounds
2)Let Alex purchase x bags @$3.21 and the remaining 14-x bags @ $ 2.64
According to the problem,
3.21x+2.64(14-x)=41.52
3.21x+36.96-2.64x=41.52
0.57x=41.52-36.96=4.56
x=8
She purchased 8 bags of candy @ $3.21
3)Let Austin collect x piees of candy
Brittany collected x-7 pieces and Anthony collected 3x+4
Therefore,
x+x-7+3x+4=57
5x=57+7-4=60
x=60/5=12
Austin collected 12 pieces

Answer 2

These questions are all about rewriting things in maths language. To do this, give everything you can think of a value like x, y and z, and then write them in terms of each other.

For example, number 3:

Call the candy that Austin collected X, Anthony's candy Y and Brittany's candy Z.

The total candy collected is 57 pieces. Writing this using maths language, you get X + Y + Z = 57.

Read the next sentence slowly, and try to keep up with it in maths language. Anthony (Y) collected 4 more than 3 times the pieces of candy collected by Austin (X). This tells you that Y = something + 4 (because he collected 4 more than that). What's the something? 3 times Austin (X).
So, Y = 3X + 4.

Do the same with the third sentence: Brittany (Z) collected 7 less than Austin (X). So, Z = X - 7.

Now you have three equations:
X + Y + Z = 57
Y = 3X + 4
Z = X - 7

Now, what letter are you looking for? Austin. That means you want to find X. So, try to get rid of the Y's and Z's from one of the equations. You can do this by substituting the values for Y (3X + 4) and Z (X - 7) into the first equation.

So, instead of X + Y + Z = 57, you write X + [3X + 4] + [X - 7] = 57. Simplify that to solve for X, and there's your answer.


Use the same technique to solve for 4. 1 and 2 also use that technique, but the maths language you need is a little more complicated, so do them last. Good luck!

Answer 3

[1] 2.25x + 3.75(2) - 2.85(x+2)
x = 3pounds

[2] 3.21x + 2.64(14-x) = 41.52
x = 8 bags of candy at $3.21

[3] x + (3x+4) + (x-7) = 57
x = 12 for Austin

[4] 9 km/hr

Answer 4

1) 225x + 2(375) = 285(2 + x)
225x + 750 = 570 + 285x
180 = 60x
x = 3 pounds

2) 321x + (14-x)264 = 4152
321x - 264x = 4152 - 14*264 = 4152 - 3696
57x = 456
x = 8

3) Let N = Anthony
A + N + B = 57
N = 3A + 4
B = A -7
A + (3A + 4) + (A- 7) = 57
5A = 60
A = 12 pieces

4) 6hrs * 8km/hr = 48 km flown all together
48 = 6*2 + 4x = 12 + 4x
36 = 4x
9 km/hr = x

Answer 5

number 1:

(x/T)($2.25/lb)+(2/T)($3.75/lb)=$2.85/lb
where T=total lbs

T=x+2;
so,
{(x/(x+2))(2.25)+(2/(x+2))(3.75)=2.85}*(x+2)
2.25x+2*3.75=2.85x+2*2.85
x=3lbs


number 2:

let x=number of $3.21 bags of candies
14-x=number of $2.64 bags of candies

$3.21x+$2.64(14-x)=$41.52

3.21x+36.96-2.64x=41.52

x=8 bags

Number 3:

Au+An+Br=57pcs ------- equation 1
An=3*Au+4 ------------- equation 2
Br=Au-7 ------------ equation 3

three equations for three unknowns

using system of linear equations... (relatively long but easy process)

Au=12pcs

Number 4:

Av.Speed=[2hrs(6km/hr)+4hrs(x)]/[6hrs]=8km/hr
where x= speed at the last 4hrs

then,

8*6=2*6+4x
x=9km/hr

Answer 6

number 3:

austin= x
anthony= 4 + 3x
brittany= x-7

x+(4-3x)+(x-7)= 57
5x-3= 57
5x= 60
x=12

Answer 7

let x pounds of candy should be added.
2.25x+2(3.75)=2.85
2.25x+7.50=(x+2)2.85
2.25x+7.50=2.85x+5.70
-0.60x=-1.80
x=3