i need help with these word problems?

Question

A)
Richard has 22 coins with a total value of $4. If the coins are all quarters and dimes, how many of each type does he have?
B)
A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100lb of mixing that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?
C)
In a town election, the winning canidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each canidate recieve?
D)The length of a rectangle is 2 in. more than twice its width. If the perimeter of the rectangle is 34in., find the dimensions of the rectangle.

Answer 1

i'm only doing A and D for you. just use these problems to guide you with the rest of your homework (:


a) to solve these kinds of problems, you need to set up a system of equations. in order to do so, make:
x= # of quarters, and y= # of dimes
so:
x+y=22, yes?

the other equation would be:
.25x + .10y=4
with these two equations, solve for x and y

1)
x + y =22
(.25x + .10y =4)100 <--to get rid of decimals

2)
(x + y = 22)-25
25x + 10y= 400

3)
-25x - 25y = -550
25x + 10y = 400 <----add up and cancel the x values, which would leave you with:

-15y = -150
so, y = 10, which really means you have 10 dimes.

to find the number of quarters (x), just plug in y=10 into an equation:
x + 10 =22, so x=12, which means you have 12 quarters.

so, the answer is 10 dimes and 12 quarters (:
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d) the formula for perimeter is 2L+ 2w, right?
well, if L = 2+2w (length is 2 in. more than 2x its width), make a system of equations:

2(2+2w) (length) + 2w = 34
4 + 4w + 2w = 34
6w = 30
w = 5 in.

now, to find the length, just plug in 5.
2 + 2(5)
2+ 10 = 12in

so, the answer is:
L = 12 in
w = 5 in


hope this helps (:

Answer 2

I will do (C) and (D) and allow others to do the rest.

Ready?

We have this one:

(C) In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive?

Set up a chart or table or an equation.

Winner = 220 more votes than the loser.

So, x + 220 = winner.

What does this mean? It means that x alone = the loser candidate.

We have this equation:

x + x + 220 = total number of votes

x + x + 220 = 810 votes

Solve for x.

2x + 220 = 810

2x = 810 - 220

2x = 590

x = 590 divided by 2

x = 295 votes for the loser.

How about the winner?

x + 220 = the winner, right?

So, replace x with 295 and then add it to 220.

295 + 220 = 515 votes for the winner.

Make sense?

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Next:

(D) The length of a rectangle is 2 inches more than twice its width. If the perimeter of the rectangle is 34 inches. Find the dimensions of the rectangle.

The perimeter of a rectangle formula is:

P = 2(length) + 2(width)

Length = 2 more than TWICE the width, which is written 2x + 2.

Width is simply just x because we do not know the width, right?

So, length = 2x + 2 and width = x.

We also know the perimeter, right?

Replace P in the formula with 34.

We now have everything we need to plug and chug.

P = 2(length) + 2(width)

34 = 2(2x + 2) + 2(x)

34 = 4x + 4 + 2x

34 = 6x + 4

34 - 4 = 6x

30 = 6x

30 divided by 6 = x

5 = x

We have this:

Width is 5 inches.
Length is 2x + 2 but we just found the value of x, right? See it?

Length = 2(5) + 2

Length = 10 + 2

Length = 12 inches

Dimensions of Rectangle:

Width = 5 inches

Length = 12 inches

Got it?

Answer 3

Do your homework yourself!! lol!! Oh just kiddin'.

A) Let q & d be numbers of quarters & dimes respectively. Then:

q + d = 22,
(0.25)q + (0.1)d = 4.

Solve that system yourself!!.

B) Let w_9 & w_12 be weights in pounds of $9-per-pound & $12-per-pound coffees respectively used in mixture. Then:

w_9 + w_12 = 100,
9w_9 + 12w_12 = (11.25)(100).

Solve that system yourself!!

C) Let w & l be numbers of votes received by winner & loser respectively. Then:

w - l = 220,
w + l = 810.

Solve that system yourself!!

D) Let l & w be length & width respectively. Then:

l - 2w = 2,
2l + 2w = 34.

Solve that system yourself!!

Answer 4

A) It can be different. This is one. 12 quarters and 10 pennies.
B) I don't know this one.
C) You need to know how much canidates there are.
D) I don't know this one.

I don't want to be mean but, try using a calqulater (however you spell it) like I did.

Answer 5

A)
25q+10d = 400
q+d = 22 => q = 22-d
25(22-d)+10d = 400
550 - 25d + 10d = 400
d = 10
q = 12

Answer 6

A)
x + y = 22
10x + 25y = 400

B)
x + y = 100
9x + 12y = 11.25*100

C)
x - y = 220
x + y = 810

D)
L = 2W + 2
2L + 2W = 34

Answer 7

a) 12 quaters and 10 dimes
b) idk
c)irdk
d)idk
srry i only got the 1st one... im only in 6th grade !