AccelePrep for the ACT Test 2nd Edition Student Text

C HAPTER 4 | F AST T RACK TO M ATH M ECHANICS • 79

9. If 3 x 2 ǡ ™Šƒ– ‹• –Š‡ ˜ƒŽ—‡ ‘ˆ x x x

x 2 2 d dn n ?

Example:

Ǥ 3 5 Ǥ 3 2 Ǥ 5 3 Ǥ 3 Ǥ 3

CLOSER LOOK ‘Ž˜‹‰ ™‹–Š ›‘—”…ƒŽ…—Žƒ–‘” is a little more time consuming in this example, „—– ‹–ǯ• ƒ ‰”‡ƒ– ƒŽ–‡”ƒ–‹˜‡ if you don’t remember Š‘™ –‘ •‘Ž˜‡ –Š‡ ’”‘„Ž‡ ƒŽ‰‡„”ƒ‹…ƒŽŽ›Ǥ STRATEGY ALERT Make sure to add the difference of squares to your „ƒ‰ ‘ˆ –‡•– †ƒ› –”‹…•Ǥ Š‹• ‹• ƒ Dz–”‹…dz „‡…ƒ—•‡ •’‘––‹‰ ‹–…ƒ •ƒ˜‡ ›‘— ’”‡…‹‘—• –‹‡Ǥ

3 2

2 3

 –Š‡ ‘–Š‡” Šƒ†ǡ Œ—•– „‡…ƒ—•‡ ›‘— Šƒ˜‡ ƒ…ƒŽ…—Žƒ–‘” ‘ ‘‡ •‡…–‹‘ †‘‡•ǯ– ‡ƒ ›‘— •Š‘—Ž† —•‡ ‹– –‘ •‘Ž˜‡ ‡˜‡”› ’”‘„Ž‡Ǥ ••—‡ ›‘— Šƒ˜‡ to do the following arithmetic to get your answer: 3 2 4 7 6 1 d d d n n n Ǥ ‹…‡ –Š‹• ‹˜‘Ž˜‡• •‹‰Ž‡ †‹‰‹– —Ž–‹’Ž‹…ƒ–‹‘ǡ ‹–ǯ• ‡ƒ•‹‡” –‘ †‘ –Š‡ ƒ”‹–Š‡–‹…„› Šƒ†ǣ 3 2 4 7 6 1 12 3 7 36 7 1 3 = = # d c d n m n Ǥ 1. Š‹• ‹–‡ –‡•–• ’”‘’‘”–‹‘• ƒ† ’‡”…‡–ƒ‰‡•ǡ ‘– †‹ˆϐ‹…—Ž–…‘…‡’–•ǡ •‘ Š‘™…‘—Ž† ‹– „‡ •‘ Š‹‰Š ‘ –Š‡ Žƒ††‡” ‘ˆ †‹ˆϐ‹…—Ž–›ǫ Š‘‹…‡ ȋ Ȍ ‹• •—…Š ƒ ƒ––”ƒ…–‹˜‡ †‹•–”ƒ…–‘” ȋ‹–ǯ• ™”‘‰ǡ „—– ‹– Œ—•– •‡‡• •‘ ”‹‰Š–Ȍǡ –Šƒ– ƒ› –‡•–Ǧ–ƒ‡”• ™‹ŽŽ ƒ—–‘ƒ–‹…ƒŽŽ› ’‹… ‹– ƒ† ‘˜‡ ‘Ǥ —– –Š‹ –Š”‘—‰Š –Š‡ ƒ–ŠǤ ”‡ƒ–‡ ƒ ’”‘’‘”–‹‘ „‡–™‡‡ –Š‡ ratio of the pre-cooked to post-cooked weights and the ratio of the …‘””‡•’‘†‹‰ ’‡”…‡–ƒ‰‡•ǡ ƒ† •‘Ž˜‡ ˆ‘” –Š‡ ’”‡Ǧ…‘‘‡† ™‡‹‰Š–ǣ x & % % x 1 100 90 90 100 9 10 1 9 1 pounds pound ’‘—†•Ǥ Š‡”‡ˆ‘”‡ǡ –Š‡ …‘””‡…– ƒ•™‡” ‹• ȋ ȌǤ 2 Ǥ Š‡ ‹–‡ •–‡ •–ƒ–‡• –Šƒ– ‡•–‡” –”ƒ˜‡Ž‡† –™‹…‡ ƒ• ˆƒ” ƒ• ƒ” ‹ ŠƒŽˆ –Š‡ –‹‡ǡ ‘” ͶͲ ‹Ž‡• ‹ ͳǤͷ Š‘—”•Ǥ Š‡ “—‡•–‹‘ ƒ•• ˆ‘” –Š‡ ƒ˜‡”ƒ‰‡ speed ǡ •‘ †‹˜‹†‡ –Š‡ –‘–ƒŽ †‹•–ƒ…‡ „› –Š‡ –‘–ƒŽ –‹‡ǡ —•‹‰ ƒ…ƒŽ…—Žƒ–‘” –‘ ƒ˜‘‹† –Š‡ ƒ”‹–Š‡–‹…ǣ 1.5 26.66 40 6 26 3 2 hours miles miles per hour, ȋ ȌǤ 3. Create an expression of ratios that, after cancellation of Ž‹‡ —‹–•ǡ ‰‹˜‡• –Š‡ —„‡” ‘ˆ…‘’‹‡• ’”‘†—…‡† ‹ ƒ hour: 10 13 1 60 1 60 seconds copies minute seconds hour minutes : : ,4 680 copies/hour ǡ ȋ ȌǤ 4. Š‡ “—‡•–‹‘ ƒ••ǡ DzŠ‘™ ƒ› •–—†‡–• ƒ”‡ǥ ϐ‹ˆ–ŠǦ‰”ƒ†‡”•ǫdz The stem also says that there are 422 students, so determine how ƒ› •–—†‡–• ƒ”‡ ϐ‹ˆ–ŠǦ‰”ƒ†‡”•Ǥ ‹…‡ ͳͺǡ ‘” ʹͲΨǡ ‘ˆ –Š‡ ϐ‹ˆ–ŠǦ‰”ƒ†‡”• „‘—‰Š– ƒ ›‡ƒ”„‘‘ǡ —•‡ –Š‹• –‘ ϐ‹† –Š‡ —„‡” ‘ˆ ϐ‹ˆ–ŠǦ‰”ƒ†‡”•Ǥ 

Answers

Return to the pages below to review each item:

1. p. 76 2. p. 76 3. p. 76 4. p. 77 5. p. 77 6. p. 78 7. p. 78 8. p. 78 9. p. 79