# 1) Find the two consecutive integers such that if we triple the first and double the second, the sum is 77. Represent: Equate: Solve: Prove: Final Answer: 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: Equate: Solve: Prove: Final Answer:

2
by MartinD

2015-01-22T21:19:23+08:00

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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
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
francis is 24 yrs old. warren is 8 yrs old. joseph is 10 yrs old.

2015-01-22T22:03:25+08:00
1.Representation:
Let x= be the first consecutive integer
x+1= be the second consecutive integer

Equate:
3x+2(x+1)=77

Solve:
3x+2x+2=77
5x+2=77

Transpose:
5x=77-2
5x=75 then divide it by 5

x=15 the first consecutive integer
x+1= the second consecutive integer
Proof:
3(15)+2(15+1)=77
5(15)+2=77
77=77

2.Representation:
Let x be Warren's age
3x be Francis age
x+2 be Joseph's age

Equate:
x+3x+x+2=42
Solve:
5x+2=42 transpose
5x=42-2
5x=40 divide by 5
x=8 Warren's age
3x=24 Francis age
x+2=10 Joseph's age

Proof:
8+24+10=42
42=42 our answers are correct :D