A retailer sells only radio and clocks. If she currently has

[christy.p.lampe]

From Algebra Study guide - Chapter 8 problem 10 on page 126

A retailer sells only radios and clocks. If she currently has 44 total items in inventory, how many of them are radios?

(1) The retailer has more than 28 radios in inventory

(2) The retailer has less than twice as many radios as clocks in inventory.


I am comfortable writing r+c=44, and r >= 29 from statement (1), but I always get mixed up when trying to write the inequality for statement number 2 (or similar problems) - my initial inequality is always 2r < c BUT the correct inequality is the reverse r < 2c


Any suggestions for how I can think about statement 2 differently so I can understand how to correctly write the inequality?

Thanks

[RonPurewal]

From Algebra Study guide - Chapter 8 problem 10 on page 126

A retailer sells only radios and clocks. If she currently has 44 total items in inventory, how many of them are radios?

(1) The retailer has more than 28 radios in inventory

(2) The retailer has less than twice as many radios as clocks in inventory.


I am comfortable writing r+c=44, and r >= 29 from statement (1), but I always get mixed up when trying to write the inequality for statement number 2 (or similar problems) - my initial inequality is always 2r < c BUT the correct inequality is the reverse r < 2c


Any suggestions for how I can think about statement 2 differently so I can understand how to correctly write the inequality?

Thanks

ha, i totally feel you on this one; i'll write these backwards about 50% of the time, too. (it doesn't help that i am dyslexic.)

here's what i do:
* forget the inequality for a sec; just consider, for a moment, the statement in which you have exactly twice as many xxxxx as yyyyy.
* think about that situation in the real world; figure out which one you have more of. (if i am on planet earth rather than in "planet classroom", and i have twice as many radios as clocks, then this means that i have more radios.)
* then write the algebra accordingly.

here, "i have twice as many radios as clocks" would be r = 2c. so, if i have fewer than that many radios, then r < 2c.

hope that helps.

[HAotian87]

Could someone please reexplain "twice as many radios as clocks". This is really confusing...

[RonPurewal]

"Twice as many xxxxx as yyyyy" means that the number of xxxxx is 2 times the number of yyyyy.

If your native language doesn't have a similar construction, then you should probably just memorize that one.