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A citrus fruit grower receives $15 for each crate of oranges [#permalink]

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25 Jan 2012, 03:42

A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped.

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped.

why cant we substitute the eq from a in to 15.(20+2G)+18G= , find g, substitute in O and get solution from (a) alone?

Last edited by Bunuel on 25 Jan 2012, 03:51, edited 1 time in total.

A citrus fruit grower receives $15 for each crate of oranges shipped and $18 for each crate of grapefruit shipped. How many crates of oranges did the grower ship last week?

Let \(x\) be the # of oranges and \(y\) the # of grapefruits. Note that \(x\) and \(y\) must be an integers. Q: \(x=?\)

(1) Last week the number of crates of oranges that the grower shipped was 20 more than twice the number of crates of grapefruit shipped --> \(x=2y+20\). Not sufficient to calculate \(x\)

(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped --> \(15x+18y=38700\) --> \(5x+6y=12900\). Multiple values are possible, for istance: \(x=180\) and \(y=2000\) OR \(x=60\) and \(y=2100\).

(1)+(2) Two unknowns, two different linear equations --> We can calculate unique value of \(x\). Sufficient.

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