Answer:
$7200 in the fund rose 6% n $2800 in the fund rose 9%
Step-by-step explanation:
let x be the amount in the fund rose 6%
gain in one year=x*6%=0.06x
total amount is 10000
so amount in the fund rose 9% = 10000-x
gain in one year=(10000-x)*9%=900-0.09x
total gain=0.06x+900-0.09x=900-0.03x
=684
900-684=0.03x
0.03x=216
x=7200
the other fund amount=10000-7200=2800
Y = -10 and x = -13 (substitute 2y + 7 for x)
Number of dimes were 81 and number of quarters were 47
<em><u>Solution:</u></em>
Let "d" be the number of dimes
Let "q" be the number of quarters
We know that,
value of 1 dime = $ 0.10
value of 1 quarter = $ 0.25
<em><u>Given that There are 128 coins in all</u></em>
number of dimes + number of quarters = 128
d + q = 128 ------ eqn 1
<em><u>Also given that collection of dimes and quarters is worth $19.85</u></em>
number of dimes x value of 1 dime + number of quarters x value of 1 quarter = 19.85
0.1d + 0.25q = 19.85 -------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
From eqn 1,
d = 128 - q -------- eqn 3
<em><u>Substitute eqn 3 in eqn 2</u></em>
0.1(128 - q) + 0.25q = 19.85
12.8 - 0.1q + 0.25q = 19.85
12.8 + 0.15q = 19.85
0.15q = 7.05
<h3>q = 47</h3>
Therefore from eqn 3,
d = 128 - q
d = 128 - 47
<h3>d = 81</h3>
Thus number of dimes were 81 and number of quarters were 47
Answer: One plain roll is 4 dollars and one shiny roll is 6 dollars.
Step-by-step explanation:
lets start by saying
rolls of plain wrapping paper = x
rolls of shiny wrapping paper = y
Kathryn sold 4 plain rolls and 3 shiny rolls for 34 dollars.
4x+3y=34
Eugene sold 4 plain rolls and 2 shiny rolls for 28 dollars
4x+2y=28
Both equations will look like this.
4x+3y=34
-1(4x+2y)=(28)-1
we can multiply the second equation by -1 to get y alone. (doesn't matter which equation). Once you do that, the positive 4x and the negative 4x cancel out, 3y-2y=1y and 34-28=6. you are left with
1y=6 so one shiny roll is 6 dollars.
now use that price to find the cost of the plain roll.
lets use Kathryn's equation
4x + 3(6)=34
4x + 18= 34
-18 -18
4x=16. Divide by 4 to find cost of one plain roll.
16÷4=4. One plain roll costs 4 dollars.
Lets check. Using Kathryn's equation,
4(4) + 3(6)=34
16+18=34
34=34. We are right.
