brain dead. math?

Question

Lane invested $22,000, part at 8% and part at 7%. If the total interest at the end of the year is $1,710, how much did she invest at 8%?
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The sum of two numbers is 33. Their difference is 9. What are the two numbers?

thanks

Answer 1

Q1
Let amount invested at 8% be x and the amount invested at 7% be $ 22,000-x

Then, interest at the end of 1 yr for x=

PRT/100 = x*8*1/100

interest at the end of 1 yr for 22,000-x=

PRT/1oo= (22,000-x)* 7 * 1/100

Now,

x*8*1/100 + (22,000-x)* 7 * 1/100 = 1710

Solving,
8x/100 + (22000-x)7/100 = 1710

Taking 100 on the other side,
8x + 7(22000-x) = 1710 *100
8x + 154000-7x = 171000
x= 171000-154000 = 17000

Ans. = $ 17000

Q2.
Let the nos. be x and y

x + y= 33 ---------(1)

When x> y
x - y = 9 -----(2)

Adding eq.1 and eq. 2
2x = 42
i.e x = 21
y= 33-21 = 12

When y> x

y-x = 9 -----(3)


Adding eq.1 and eq. 3

2y = 42
y = 21
x= 12

Ans. The nos are 12 and 21

Answer 2

Lane invested $22,000, part at 8% and part at 7%. If the total interest at the end of the year is $1,710, how much did she invest at 8%?
let x= amt invested at 8%
1710=.08x+.07 (22000-x)
1710=0.08x+1540-.07x subtract 1540 from each side
170=.01x multiply both sides by 100
17000=x
Lane invested $17,000 at 8% and
22000-17000=$5,000 at 7%

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The sum of two numbers is 33. Their difference is 9. What are the two numbers?

x+y=33
x-y=9 add
2x=42 divide both sides by 2
x=21
21-y=9
subtract 21 from each side
-y=-12 multiply both sides by -1
y=12

the numbers are 21 & 12

Answer 3

I am working out on the second problem
let the two numbers are a, b
so according to the problem
a+b=33 And
a-b=9 now adding the both equation will give you
2a=42
so a=21
hence b=33-21
=12

Answer 4

let's call the two parts a and b
a+b=22000
.08a + .07b = 1710
you can solve for both a and b, but you only need to find a

multiply first equation by .07 and subtract from second equation
.01a = 1710 - .07*22000 = 170
a = 17,000
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a+b=33
a-b=9
add the equations: 2a=42, a=21,
and then b=33-a = 33-21 = 12

Answer 5

x(0.07) + (22000-x) (0.08) = 1710. Solve for x.
x + y = 33; x - y = 9; x = 21 and y = 12.

Answer 6

i can help u with the first one, i learned bout em last week lol though ive turned pro lol
well here it goes:
0.08 + 0.07(22,000-x)= 1710
0.08 + 1540 - 0.07x= 1710
0.01x +1540 =1710
0.01x = 170
x= $17,000 and $5000
hope that helped sorry that i cant help with the other one

Answer 7

21
12