Victory for the ACT Student Text 15e

260 • M ATH

EXPLANATIONS

5. •–—†‡– „‡‰‹• Š‡ƒ–‹‰ ƒ…‡”–ƒ‹ substance with a temperature of 50°C over a Bunsen burner. If the temperature ‘ˆ –Š‡ •—„•–ƒ…‡ ™‹ŽŽ ”‹•‡ ʹͲι ˆ‘” ‡˜‡”› 24 minutes it remains over the burner, ™Šƒ– ™‹ŽŽ „‡ –Š‡ –‡’‡”ƒ–—”‡ǡ ‹ †‡‰”‡‡• Celsius, of the substance after 18 minutes? Ǥ ͷʹ B. 56 C. 60 D. 65 E. 72 ˆ –Š‡ ”ƒ–‹‘ ‘ˆ ƒ’’Ž‡• –‘ ‘”ƒ‰‡• ‹ ƒ ˆ”—‹– •ƒŽƒ† ƒ†‡ ‘ˆ ‘Ž› –Š‘•‡ –™‘ ˆ”—‹–• ‹• ͺ to 7, what fractional part of the salad is ‘”ƒ‰‡•ǫ F. 56 1 G. 15 1 H. 7 1 J. 15 7 K. 7 8 7. Ž‘…ƒŽ…ƒˆ‡ Šƒ• ƒ •‘—’ ƒ† •ƒŽƒ† Ž—…Š special. There are three soups and six •ƒ†™‹…Š• ƒ˜ƒ‹Žƒ„Ž‡Ǥ ‘™ ƒ› †‹ˆˆ‡”‡– soup and salad combinations are possible? Ǥ ʹ B. 3 C. 9 D. 12 E. 18 Š‡ ƒ˜‡”ƒ‰‡ ™‡‹‰Š– ‘ˆ –Š”‡‡ „‘š‡• ‹• 25 3 1 ’‘—†•Ǥ ˆ ‡ƒ…Š „‘š ™‡‹‰Š• ƒ– Ž‡ƒ•– 24 pounds, what is the ‰”‡ƒ–‡•– possible ™‡‹‰Š–ǡ ‹ ’‘—†•ǡ ‘ˆ ƒ› ‘‡ ‘ˆ –Š‡ „‘š‡•ǫ F. 25 G. 26 H. 27 J. 28 K. 29 6. 8.

5. (D) Mathematics/Number and Quantity/ Rates and Proportions Š‡ Ž‘‰‡” –Š‡ •—„•–ƒ…‡ ‹• Š‡ƒ–‡†ǡ the hotter it will be, so the quantities demonstrate direct variation: & & minutes C y x y x x 24 20 18 minutes C 1 1 2 2 c c c Thus, the new temperature is 50 15 65 C c c c + = . 6. (J) Mathematics/Number and Quantity/ Rates and Proportions ‹’Ž‹ˆ› –Š‡ ‹–‡ „› ƒ••—‹‰ –Š‡”‡ ƒ”‡ ‡šƒ…–Ž› ͺ ƒ’’Ž‡• ƒ† ͹ ‘”ƒ‰‡• ‹ –Š‡ salad. Therefore, 15 pieces of fruit are in –Š‡ •ƒŽƒ†ǡ ƒ† –Š‡ ‘”ƒ‰‡• ƒ”‡ 15 7 of the total number. . min min utes utes 24 20 15 C 18 C # c

Throwback to Math Class Š‡ •‡––‹‰ —’ proportions, a common technique –‘ •‘Ž˜‹‰ ˆ‘” ƒ —‘™ ‹• …”‘••Ǧ—Ž–‹’Ž›‹‰ǡ ”‘••Ǧ—Ž–‹’Ž›‹‰ ‹• ™Š‡ ›‘— —Ž–‹’Ž› –Š‡ numerator of the ϐ‹”•– ˆ”ƒ…–‹‘ ™‹–Š the denominator of the second and denominator of the ϐ‹”•– ˆ”ƒ…–‹‘ ™‹–Š the numerator of the second and set both products equal to each other. ”‘••Ǧ—Ž–‹’Ž›‹‰ eliminates the fractions and returns an equation that ‹• ‡ƒ•› –‘ •‘Ž˜‡ ƒŽ‰‡„”ƒ‹…ƒŽŽ›Ǥ

7. (E) Mathematics/Statistics and Probability/Counting Methods

For each of the three soups, there are six possible sandwiches—the total number of combinations is 3 6 18 : .

8. (J) Mathematics/Statistics and Probability/Measures of Center

Š‡ ƒ˜‡”ƒ‰‡ ™‡‹‰Š– ‘ˆ –Š‡ –Š”‡‡ „‘š‡• ‹• 25 3 1 ’‘—†•ǡ •‘ –Š‡ –‘–ƒŽ ™‡‹‰Š– ‘ˆ –Š‡ „‘š‡• ‹• ͹͸ ’‘—†•Ǥ ˆ ‡ƒ…Š „‘š ™‡‹‰Š• at least 24 pounds, then the minimum ™‡‹‰Š– ‘ˆ –™‘ „‘š‡• ‹• Ͷͺ ’‘—†•ǡ ƒ† –Š‡ ƒš‹— ™‡‹‰Š– ‘ˆ ƒ› ‘‡ „‘š ‹• 76 48 28 − = pounds.