Maricopa's Success scholarship fund receives a gift of $ 90,000. The money is invested in stocks, bonds, and CDs. CDs pay 4.25% interest, bonds pay 4.3% interest, and stocks pay 8.6% interest. Maricopa Success invests $30,000 more in bonds than in CDs. If the annual income from the investments is $5,153 , how much was invested in each account?

Let us assume Maricopa invested X amount in CDs, then she would have invested X+30000 in bonds

We know Amount Invested in CDs + Amount invested in Bonds + Amount Invested in Stocks = 90000

As we earlier discussed Amount Invested in CDs = X, Amount Invested in X + 30000 putting these in above equation

X + X + 30000 + Amount invested in stocks = 90000

2X+ 30000 + Amount invested in stocks = 90000

Taking 2X + 30000 to right hand side of equation  

Amount invested in stocks = 90000 - 30000 - 2X

= 60000 - 2X

Now Interest on CDs = 4.25 % * Amount invested in CDs = 4.25/100 * X =  0.0425 X

Interest on bonds = 4.3/100 % * Amount invested in Bonds = 4.3/100 * (30000 + X)= 1290 + 0.043X  

Interest on stocks = 8.6/100% * Amount invested in stocks = 8.6/100 * (60000 - 2X) = 5160 - 0.172X

Total Interest = 5153

Adding all the interest calculated

0.0425X + 1290+ 0.043X + 5160 - 0.172X = 5153

(0.0425X + 0.043X - 0.172X) + (1290+5160) = 5153

-0.0865 X + 6450 = 5153

0.0865 X = 6450 - 5153

0.0865 X = 1297

X = 15000

CDs amount = $15000

Bonds amount = $45000

Stocks amount = $30000

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions