Question

Do a and b have the same value in the equations 2(a-1.1)=5.8 and 5/2b-2 3/4=7 1/4

Answer 1

Yes, a and b have the same value in the given equations.

Explanation:

Equation 1

`2(a-1.1)=5.8`

`\implies 2a-2.2=5.8`

`\implies 2a-2.2+2.2=5.8+2.2`

`\implies 2a=8`

`\implies (2a)/(2)=(8)/(2)`

`\implies a=4`

Equation 2

`(5)/(2)b-2(3)/(4)=7 (1)/(4)`

`\implies (5)/(2)b-(2 * 4+3)/(4)=(7 * 4+1)/(4)`

`\implies (5)/(2)b-(11)/(4)=(29)/(4)`

`\implies (5)/(2)b-(11)/(4)+(11)/(4)=(29)/(4)+(11)/(4)`

`\implies (5)/(2)b=(40)/(4)`

`\implies (5)/(2)b=10`

`\implies 2 \cdot (5)/(2)b=2 \cdot 10`

`\implies 5b=20`

`\implies (5b)/(5)=(20)/(5)`

`\implies b=4`

Conclusion

As a = 4 and b = 4, the two variables have the same value in the given equations.

Answer 2

• Yes

Explanation:

Solve each equation and compare the solutions

1.

• 2(a - 1.1) = 5.8
• a - 1.1 = 5.8/2
• a - 1.1 = 2.9
• a = 2.9 + 1.1
• a = 4

2.

• (5/2)b - 2 3/4 = 7 1/4
• 2.5b = 7 1/4 + 2 3/4
• 2.5b = 10
• b = 10/2.5
• b = 4

Both a and b have same value