Algebra word problem?

bravo-my-friend

Please show work if you can:

1) $5,900 is invested, part at 11% and part of it at 6%. For a certain year, the total yield is $509.00. How much was invested at each rate?

2) How much 75 octane and 90 octane gas is needed to make 15 gallons of 87 octane gas?

polygon

Let x = amount invested at 11%

1)...A1 = x(1.11)

2)...A2 = (5900 - x)(1.06)

2) ...A2 = 6254 - 1.06x

Total return = 5900 + 509 = 6409

A1 + A2 = 6409

3) 6409 = 1.11x + 6254 - 1.06x

155 = 1.05x

x = $147.62 invested at 11%

$361.38 invested at 6%

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Let x = gallons of 75 octane gas

75x + 90(15 - x) = 87*15

75x + 1350 - 90x = 1305

-15x = - 45

x = 3 gallons of 75 octane

12 gallons of 90 octane

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