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4 years ago

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Baseball Ichiro Suzuki holds the American League record for the most hits in a single baseball season. In 2004, Suzuki had a tot

al of 262 hits for the Seattle Mariners. He hit three fewer triples than home runs, and he hit three times as many doubles as home runs. Suzuki also hit 45 times as many singles as triples. Find the number of singles, doubles, triples, and home runs hit by Suzuki during the season.

1 answer:

mamaluj [8]4 years ago

7 0

Let Home runs = X

Triples would be X-3 ( 3 less triples than home runs)

Doubles would be 3x ( 3 times as many doubles as home runs)

Singles would be 45(x-3) ( 45 times as many singles as triples)

Simplify the equation for singles to be 45x-153

Now you have X + x-3 + 3x + 4x-135 = 262

Simplify:

50x - 138 = 262

Add 138 to both sides:

50x = 400

Divide both sides by 50:

x = 400/50

x = 8

Home runs = x = 8

Triples = x-3 = 8-3 = 5

Doubles = 3x = 3(8) = 24

Singles = 45(x-3) = 45(8-3) = 45(5) = 225

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Answer:

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<u>FORMULAES TO KNOW BEFORE SOLVING :-</u>

$\sin \theta = \frac{Side \: opposite \: to \: \theta}{Hypotenuse}$
$\cos \theta = \frac{Side \: adjacent \: to \: \theta}{Hypotenuse}$
$\tan \theta = \frac{Side \: opposite \: to \: \theta}{Side \: adjacent \: to \: \theta}$

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1) θ = 16°

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$=> x = \frac{6}{0.48480....} = 12.37599.....$ ≈ 12.3

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5) θ = 55°

Length of side adjacent to θ = x

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Length of side adjacent to θ = 8

Hypotenuse = x

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7) θ = 69°

Length of side opposite to θ = 12

Length of side adjacent to θ = x

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$=> \frac{12}{x} = 2.60508......$

$=> x = \frac{12}{2.60508....} = 4.60636....$ ≈ 4.6

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Length of side opposite to θ = 11

Length of side adjacent to θ = x

$=> \tan 20 = \frac{11}{x}$

$=> \frac{11}{x} = 0.36397......$

$=> x = \frac{11}{0.36397....} =30.22225....$ ≈ 30.2

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