224 A-plus notes for beginning algebra EXERCISES Hint: We can find the solutions of most of the following word problems either by using one equation with one variable or by using a system of two equations. Here you should practice to find the solutions by using a system of two equations. Assign two variables to represent the two unknowns. 1. John has twice as much money as David. Together they have $156. How much money does each have ? 2. There are one-dollar bills and five-dollar bills in the piggy bank. It has 64 bills with a total value of $244. How many ones and how many fives in the piggy bank ? 3. There are quarter and dimes in a box. Their total value is $5.40. Quarters are five times as many as dimes. How many quarters and how many dimes are in the box ? 4. Flying with the tail wind, an airplane flies 860 km per hour. Flying with the same wind, it flies 740 km per hour to make the return flight against the wind. Find the speed of the wind and the speed of the airplane. 5. Twice a number is 20 more than another number. One fourth of the first number is 29 less than the second number. Find the two numbers. 6. You want to rent a vehicle for one day. The rental cost for a car is $65 plus $0.25 per mile. The rental cost for a truck is $110 plus $0.10 per mile. How many miles that you travel will cost the same for both options ? 7. The width of a rectangle is 12 cm shorter than the length. The perimeter is 52 cm . What is the dimensions of the rectangle ? 3. The width of a rectangle is 15 in. shorter than twice the length. The perimeter is 45 in.. What is the dimensions of the rectangle ? 9. In a school fair, Roger bought hamburgers at a cost of $9 per dozen and bagels at a cost of $3 per dozen. He bought a total of 45 dozens and paid a total of $255. How many dozens of hamburgers and how many dozens of bagels did he buy ? 10. Two hamburgers and one bagel cost $4.70. At the same prices, one hamburger and two bagels cost $3.70. How much does each hamburger and each bagel cost ? 11. In a school fair, John bought 30 boxes of hamburgers and bagels. Each box contains 20 hambergers. Each box contains 25 bagels. A total of 690 hamburgers and bagels was bought. How many boxes of hamburgers did he buy ? How many boxes of bagels did he buy ? 12. A balloon at 900 feet high is descending at a rate of 4 feet per second. Mother balloon is rising from the ground at a rate of 2 feet per second. In how many seconds will the two balloons be at the same altitude ? 13. A teacher distributes a box of pencils to the students. If each student receives 4 pencils, there are 8 pencils left. If each student receives 5 pencils, there are 20 pencils short. How many students are there ? How many pencils are in the box ? 14. You have a $20 bill. If you buy 24 pens and 12 pencils, you will get $1.40 change. If you buy 12 pens and 24 pencils, you will get $4.40 change. How much does each pen and eac114 4 pencil cost ? 15. There are 3,192 students in Hawthorne High School. There are 168 more boys than girls. How many boys and how many girls are there ? te0 ra VrO\Abete\ S &AC, s-4:\ k- TS 7o1/49\i\ (1%/\ 1,10A 2Di-DT-ISCo ar o = Icco lb tt 1;to ~~ s z CkeC. ni3 7-(52) 10 Li ® z1 I Bids F. 4 C- 104 4 Sz- ts(, 7 Ek07 1/4,AteCtad\ is -\-x z (Dit (1 ks 7 k - z 6 10 NSF - (09 4-SF= 2)-0-1 LIF ItO LI `A z LtS Chest KVA4k) \- KS -,(0(-1 5@s) -cvei ✓ 1\ --- ef 5 ReS b .11,0 G-ccD (74 t~k44;0 . Zs(sts)k-.1ot =si-to 1.2s D .lo t. ts- z LID 1.(K3 ktaLt & sCy CV\ ect • Zs (20) 1- slo(9)= S,9 Zo = SC4) W .= t,`), &C sped f>101/4/1/4t 'r4 ? N., aon EV.■ no S t -Vv.) -11/4ko k") 4- 460 t- e t $00 (.1/43 r- 600:1 beck 1 :00 t4) z- lct o ?ft Ckc LtC -c- V00 'goo k bolt c 46(0 V top- too r- "Pio / z 0 X 'c 15C- it ZAtt 3;t )( 1'4 "VW 471 ZO -j = *V‘ -j x= 18 '0= i -l ek 1(1 it tC0 -7 1= 5 -1 36 CL') C Cc r- to( 4,-T 7 r %Xt. (-05- Ct ‘s A. ,25+1/4,\ t -1c-•11)K C,C k .2Ssoo) z Ltjo , 10c5_50) T Lto ✓ r ck 2(1) Z0 4-3 (0 ✓ a 3 b -VI 1/4/ a \A A k ‘-k r- \101413,"3 cf OA 4 113 3.70 Ca5C..\ zvk 1 z :.- yip ...s? k VS= 14-1° z_z 3:10) AS 7-'140 ct 0 \ z YID • c‘Lectc, z trio' ,--/D.,-licto “:_to)z i It ,k_ 60,L13 0- k ' ZIA+ %-%451 z)c- .: oAecic tz Jr-18 = 30 zo Q:01:0zs) 4010‘7 \Az heIkk.€ \*r- ¶00 " ' Cat° t-1 ntA;k-ia, Zo C7-t, Ait 2041k-t.SZzklb -20 -100 —3 —3 .ftC2 13 F Sib Sk-kko-kto r. {)ekeAls CLOcic k 20 Qiic6 Pz- ()CAS L_ = 21\ p It. 60 ic.(00 L ? frUfk.c.t-U3e\ 11'4) kV- L 7:- (100 .= Is-. (a 0) Vile V. L 7- IC. 60 - 11, 7 o L 7.1\e 4 ZAP ( ktec_k 2LA cle0) VZ- @IC) VZOCY4t ,6° kZ 7-IAOS 1` ,150 2- -L r 7_ Sitkiiis0 Z- lit Li (DO 2- 1A V& 6O 60 " Buys CR`--ls % sr z Vt -z_ A--110c6 \1/41 iN CLect.1/4 t."Z_ V680 31°12.± 1660 = 15‘2. — \b \S 1Z st-.- 31`11_ -As- Az -As- kL t -1660 —Ito --St°