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1) Find the two consecutive integers such that if we triple the first and double the second, the sum is 77.
Represent: x first integer x+1 second integer Equate: 3x+2(x+1)=77 Solve: 3x+2x+2=77; 5x=75; x=15 Prove: 3(15)+2(15+1)=77; 45+32 = 77; 77 = 77 Final Answer: 15 and 16

2) Francis is thrice as old as Warren. Joseph is 2 years older than Warren. If the sum of their ages is 42, find the ages of the three boys.

Represent: x age of francis y age of warren z age of joseph Equate: x=3y; z=y+2; x+y+z=42 Solve: (3y)+y+(y+2)=42; 5y=40; y=8; x=24; z=10 Prove: 24=3(8); 24 = 24; 10=8+2; 10 = 10; 8 + 24 + 10 = 42; 8 + 24 + 10 = 42 Final Answer: francis is 24 yrs old. warren is 8 yrs old. joseph is 10 yrs old.