Answer: [tex]\Large\boxed{27}[/tex]
Step-by-step explanation:
Given information converted into a mathematical statement
[tex]a = icecream\\b=cookie\\c=brownie\\d=cake\\e=creamed cake[/tex]
[tex]1)~a+b+a+b=42[/tex]
[tex]2)~c+d+c=35[/tex]
[tex]3)~c+c+e=29[/tex]
[tex]4)~a+d+b-e=\mbox{?}[/tex]
Simplify each equation
[tex]1)~2a+2b=42[/tex]
[tex]2)~2c+d=35[/tex]
[tex]3)~2c+e=29[/tex]
[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]
Factorize 2 out of the 1) equation
[tex]2a+2b=42[/tex]
[tex]2(a+b)=42[/tex]
Divide 2 on both sides
[tex]2(a+b)\div2=42\div2[/tex]
[tex]a+b=21[/tex]
Current system
[tex]1)~a+b=21[/tex]
[tex]2)~2c+d=35[/tex]
[tex]3)~2c+e=29[/tex]
[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]
Subtract 3) equation from the 2) equation
[tex](2c +d)-(2c+e)=(35)-(29)[/tex]
Expand the parenthesis
[tex]2c+d-2c-e=35-29[/tex]
Combine like terms
[tex]2c-2c+d-e=6[/tex]
[tex]d-e=6[/tex]
Current system
[tex]1)~a+b=21[/tex]
[tex]2)~d-e=6[/tex]
[tex]3)~(a+b)+(d-e)=\mbox{?}[/tex]
Substitute values into the 3) equation to determine the final value
[tex](a+b)+(d-e)[/tex]
[tex]=(21)+(6)[/tex]
[tex]\Large\boxed{=27}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
