Thread: Algebra 1 Urgent HW Help

Hi everybody. I have a few math questions that I need urgent help on. You don't have to do all, but can you please do the ones that you want to/can do?
Please include the steps of how you got the answer. Thanks so much!
If you can solve any by using different directions, feel free to do so.

Solve by the substitution method.
18. (y/2) - x = 1
x+y+7=0

22. 3b - 2a = 4
b/2 - (2a/3) = 1

26. a + b = 5000
0.08a = 0.06b - 20

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Use n, d, and q for the # of nickels, the number of dimes, and the number of quarters, respectively.

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?

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Solve, using two equations in two variables.

14. If you buy 6 pens and one mechanical pencil, you'll get only $1 change from your $10 bill. But if you buy 4 pens and 2 mechanical pencils, you'll get $2 change. How much does each pen & each pencil cost?

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.

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?

20. If Bill rides his bike 3 mi to Fred's house & then walks with Fred the remaining 1 mi to school, it will take him 30 min. But if he rides the entire distance, it will take him only 20 min. Find his biking speed and walking speed.

22. Carl, Diane, & Ed together have $46. Carl has half as much as Diane, and Ed had $2 less than Diane. How much does each have?

Thanks again!

Hello, vanilla_yum!

Here are a few of them . . .

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?

Julia has x quarters. .She has 25x cents.

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

"Julia has 180¢ more than Luis."
There is our equation: .25x .= .10x + 180

Solve for x . . .

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.

Let x = amount invested at 6%.
. . 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)