Less Longer

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Less Longer
Less Longer
One integer is 8 less than 4 times another longer integer. The product of the two integers is 60. What are the?


Math question continued below:

One integer is 8 less than 4 times another longer integer. The product of the two integers is 60. What are the two integers? Solve the problem algebraically. Show all work.

I'm pretty sure there's no solution as the problem is stated.

Call the smaller integer S, the longer one L.

"One integer is 8 less than 4 times another longer integer"
S = 4L - 8

"The product of the two integers is 60"
L*S = 60

Solve the two equations simultaneously by whatever method looks best. I'd go with:
L(4L - 8) = 60
4L^2 - 8L = 60
L^2 - 2L - 15 = 0
And factorise to solve for L.

This gives L=5, S =12 or L=-3, S=-20

L=5, S=12 isn't a solution because L isn't a "longer" integer than S.
L=-3, S=-20 isn't a solution because -3 isn't a "longer" integer than -20. It would be if the question means "greater" rather than "longer".



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The Czars' debut full-length release on Robin Guthrie and Simon Raymonde's (of the Coceteau Twins) Bella Union imprint is a stunning, rocking electro-folk album of controlled restraint. Vocalist and chief songwriter John Grant's emotional lyrics and singing style evoke a dark, poetic imagery throughout the album's 11 tracks. One of the standout tracks is "Val," where Grant sings a brittle, deep-throated ode to emptiness. With Paula Frazer, of Tarnation, providing backup vocals against Grant's commanding inflections, the album burns slowly through track and after track of percolating electronic sound foundations. "Gangrene" brings to mind a less gruff Mark Lanegan track, as it picks up steam toward a finale of intense guitar play. "Get Used to It" is an enjoyably sarcastic song detailing a personal worldview that leads to depression; it exudes a charming catchiness. Late into the song, Frazer's vocals bring to mind Ennio Morricone's soundtrack to Once Upon a Time in the West. "Dave's Dream" is a pretty, calming number, followed immediately by "What I Can Do For You," a song which seems too catchy on first listen, before becoming an absolute joy afterwards. "Zippermouth" takes a more aggressive tone, with Grant becoming downright angry about a boring relationship, while the rest of the band gets into a dark groove; despite the harsh tone, Grant eventually expands his vocals into a lilting falsetto, giving the song the needed contrast to validate its placement on the album. It is not hyperbole to suggest that Before...But Longer is the sort of album that demands repeat listens; indeed, it becomes hard to listen to anything else. Since the album is remarkably subtle, its charms are virtually impossible to ignore. The Czars astound again and again on this album. ~ Tim DiGravina, RoviPerformers: Paula Frazer - Vocals, Voices; John Grant - Piano, Vocals, Voices; Jeff Linsenmaier - Drums, Guitar; Andy Monley - Guitar

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The Paradox of Choice - Why More Is Less

How long does Hydro stay in your system? Is it less, longer, or the same time as regular bud?


I need to know how long it is in your system and if there is anything good to do to help the detox process along.

There is this drink, wait can I even answer this? Ok, my apologies yahoo if I wasn't supposed to. There is a drink, the bottle says natural cleanser, you drink the whole bottle, like 16oz, then fill the bottle with water. Wait how ever long they tell you and drink another bottle. You have to get tested, which is what I will assume you need to do. You have to do in it within a three hour period for maximum effect. It costs $45. at any head shop. Oh yeah, don't ever buy the one from GNC, they test for it!

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