Math Help - A few College Algebra questions

1. A few College Algebra questions

Hello Math Help Forum!

Determine how many solutions exist-
Use either elimination or substitution to find the solutions (if any)
1) 4x = 8 and 5y = 15

I was thinking the solution was at (2,3) but I don't know how to use elimination or substitution to show that.

2. An express and local train leave Grays Lake at 3 P.M. and head for Chicago 50miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

I am stumped on this one.

3. On the first day of school, the percentage of boys in a particular class is 60%.During the school year, six girls move away, and are replaced in the class by six boys; this makes the class roster 75% boys. Find the number of boys and girls in the class on the first day of school.

Help on any of these will be greatly appreciated!

2. Originally Posted by MathGeek06
Hello Math Help Forum!

Determine how many solutions exist-
Use either elimination or substitution to find the solutions (if any)
1) 4x = 8 and 5y = 15

I was thinking the solution was at (2,3) but I don't know how to use elimination or substitution to show that.

2. An express and local train leave Grays Lake at 3 P.M. and head for Chicago 50miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

I am stumped on this one.

3. On the first day of school, the percentage of boys in a particular class is 60%.During the school year, six girls move away, and are replaced in the class by six boys; this makes the class roster 75% boys. Find the number of boys and girls in the class on the first day of school.

Help on any of these will be greatly appreciated!
Comments for the questions as indicated:

1. Your answer is correct. You don't use substitution or elimination. You just solve each equation seperately.

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2. Let speed of local train = x and let time taken by local = t. Note that they both travel the same distance (50 km). Then:

Local train: xt = 50 .... (1)

Express train: 2x(t - 1) = 50 => 2xt - 2x = 50 .... (2)

Sub (1) into (2) and solve for x.

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3. Let no. of boys on first day = b and number of girls on first day = g. Note that b + g = no. of students in class stays the same over the whole year. Then:

$\frac{b}{b + g} = \frac{6}{10} \Rightarrow 10 b = 6 (b + g) \Rightarrow 4b = 6g$ .... (1)

Note that 60% is equivalent to 6/10.

$\frac{b+6}{b + g} = \frac{3}{4} \Rightarrow 4(b + 6) = 3 (b + g) \Rightarrow 4b + 24 = 3b + 3g \Rightarrow b = 3g - 24$ .... (2)

Note that 75% is equivalent to 3/4.

Sub (2) into (1) and solve for g. Once you know g, sub its value into (1) and solve for b.