Hello, vanilla_yum!

Here are a few of them . . .

Julia has x quarters. .She has 25x cents.6. Luis & Julia have the same number of coins.

Luis has only dimes and Julia has only quarters.

If Julia has $1.80 more than Luis does, how many coins does each have?

Luis has x dimes. .He has 10x cents.

"Julia has 180¢ more than Luis."

There is our equation: .25x .= .10x + 180

Solve for x . . .

Let x = amount invested at 6%.16. Melina Bowen receives an annual income of $234.50 from investing

one amount of money at 6% and another amount at 5%.

If the investments were interchanged, her income would increase by $5.10.

Find the amounts she invested.

. . Her interest is: 0.06x dollars.

Let y = amount invested at 5%.

. . Her interest is: 0.05y dollars.

Her total interest is $234.50: .0.06x + 0.05y .= .234.50

If the investments were interchanged . . .

She invested x dollars at 5%.

. . Her interest would be: 0.05x dollars.

She invested y dollars at 6%.

. . Her interest would be: 0.06y dollars.

Her total interest would be $5.10 more: .$234.50 + 5.10 .= .$239.60

The equation is: .0.05x + 0.06y .= .239.60

Solve the system of equations:

. . 0.06x + 0.05y .= .234.50

. . 0.05x + 0.06y .= .239.60

I would multiply the equatons by 100 to eliminate those annoying decimals.

. . 6x + 5y .= .23450

. . 5x + 6y .= .23960

(I got: x = 1900, y = 2410)

18. A grocer mixes together some cashews costing $8 per kilogram

with some Brazil nuts costing $10 per kilogram.

The grocer sold 12 kg of the mixture for $8.50 per kilogram.

How many kilograms of cashews were in the mixture the grocer sold?

Let C = number of kg of cashews.

Let B = number of kg of Brazil nuts.

The grocer sold 12 kg of the mixture: .C + B .= .12

The C kg of cashews are worth 8C dollars.

The B kg of Brazil nuts are worth 10B dollars.

. . Their total value is: 8C + 10B dollars.

The grocer sold 12 kg @ $8.50 per kilogram.

. . He received: .12 × $8.50 .= .$102

We have another equation: .8C + 10B .= .102

Solve the system:

. . .C + . B . = .12

. .8C + 10B .= 102

(I got: C = 9, B = 3)