Some word problems that I can not figure out.?

Question

1)Donna invested her 33,000 bonus and received a total of 970 in interest after one year. If part of the money returned 4% and the remainder 2.25% then how much did she invest at each rate?

2)at gwens garage sale all books were one price, and all magazines were another price. Harriet bought four books and 3 magazines for 1.45, and june bought 2 books and 5 magazines for 1.25. what was the price of a book and what was the price of a magazine?

3) Ziggys famous yogurt blends regular that is 3% fat with its no fat yogurt to obtain low fat yogurt that s 1% fat. How many pounds of regular yogurt and how many pounds of no fat yogurt should be mixed to obtain 60lbs of low fat yogurt?

4)the probability that the san francisco plays in the next super bowl is 9 times the probability that they do not play in the next super bowl. the probability that they play in the super bowl plus the probability that they do not play is 1. what is the probability that they play in the next super bowl?

Answer 1

1) First ones done.

2)Let all books be $x, and
Let magazines be $y.
Harriet bought four books and 3 magazines for 1.45,

So, 4x + 3y = 1.45

and june bought 2 books and 5 magazines for 1.25.

So, 2x + 5y =1.25

From 2x equation 2 subtract equation 1 .
7y = 2.50 -1.45
7y = 1.05
y = 0.15

From equation 2 substitute this value for y.
2x =1.25 - 5x0.15
2x = 0.5
x=0.25

So the price of a book was $0.25 and the price of a magazine was $0.15?

3) Ziggys famous yogurt blends regular that is 3% fat with its no fat yogurt to obtain low fat yogurt that s 1% fat. How many pounds of regular yogurt and how many pounds of no fat yogurt should be mixed to obtain 60lbs of low fat yogurt?

I'll get back to this one - got to go

Back again:
Let amount of 3% yogurt be x
Let amount of 0% yogurt be y
So, x+y =60
And, .03x/(x+y) =0.01
0.03 x =0.01 (x+y)
3x = x+y
2x=y
Substitute this back in the first equation.
x+2x =60
x=20 lb
so, y=40 lb

4) Let the probability that the san francisco plays in the next super bowl be 9x.
This is 9 times the probability that they do not play in the next super bowl.
So the probability that they do not play in the super bowl is x.
x +9x =1
10x=1
x=1/10
The probability that they play in the next super bowl is 1/10.

Answer 2

1)Donna invested her 33,000 bonus and received a total of 970 in interest after one year. If part of the money returned 4% and the remainder 2.25% then how much did she invest at each rate?
y = 33,000-x
970 = 0.04*x + 0.0225*y
970 = 0.04x +0.0225(33,000-x)
970 = 0.04x - 0.0225x + 742.5
970-742.5 = 0.0175x
x = 227.5 / 0.0175 = 13000
y = 20000

Answer 3

x = amount at 4%
33,000-x = amount at 2.25 %
.04x +.0225(33000-x) = 970
.04x + 742.5 -.0225x = 970
.0175x = 227.5
x = 13,000 = amount at 4%
33000-x = 20,000 = amount at 2.25%

4B +3M = 1.45
2B + 5m = 1.25
-4B -10M= -2.50
-7M = -1.05
M= .15 dollars = 15 cents
2B +.75 =1.25
B = .25 dollars = 25 cents

40 pure+ 20 at 3%

P= 9(1-P)
P=9 -9P
10P = 9
P= .9