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)