We are asked which of the given combinations will produce a number that is less or equal to 25.
For A we have:
[tex]A=3(8\frac{3}{4})[/tex]Let's remember that for a mixed fraction we have:
[tex]a\frac{b}{c}=a+\frac{b}{c}[/tex]Therefore, we can change the mixed fraction and we get:
[tex]A=3(8\frac{3}{4})=3(8+\frac{3}{4})[/tex]Solving the operations:
[tex]A=26.25[/tex]Since we get a number greater than 25 this is not a trail he can ride.
For B we have:
[tex]B=2(10\frac{1}{4})[/tex]Changing the mixed fraction:
[tex]B=2(10\frac{1}{4})=2(10+\frac{1}{4})[/tex]To solve the operation we will apply the distributive property:
[tex]B=20+2\times\frac{1}{4}[/tex]Now, we simplify the fraction:
[tex]B=20+2\times\frac{1}{4}=20+\frac{1}{2}[/tex]Now, we use the fact that 1/2 = 0.5:
[tex]B=20+\frac{1}{2}=20+0.5=20.5[/tex]Since we get a number that is less than 25 this is a train he can ride.
For C we have:
[tex]C=2(7\frac{1}{2})+10\frac{1}{4}[/tex]Changing the mixed fraction:
[tex]C=2(7+\frac{1}{2})+10+\frac{1}{4}[/tex]Now, we apply the distributive property:
[tex]C=14+1+10+\frac{1}{4}[/tex]Solving the operations. We use the fact that 1/4 = 0.25:
[tex]C=25+0.25=25.25[/tex]Since we get a number greater than 25 this is not a trail he can ride.
For D.
[tex]D=7\frac{1}{2}+2(8\frac{3}{4})[/tex]Now, we change the mixed fractions:
[tex]D=7+\frac{1}{2}+2(8+\frac{3}{4})[/tex]Now, we use the distributive property:
[tex]D=7+\frac{1}{2}+16+2\times\frac{3}{4}[/tex]Simplifying the fraction:
[tex]D=7+\frac{1}{2}+16+\frac{3}{2}[/tex]Now, we add the fractions, we have into account that when fractions have the same denominator we can add the numerators and use the common denominator, like this:
[tex]D=7+\frac{4}{2}+16[/tex]Simplifying the fraction we get:
[tex]D=7+2+16[/tex]Solving the operations:
[tex]D=25[/tex]Since we get 25 this is a trail that he can ride.
