Fraction

[shadali]

1) 1/6 of John's weight is equal to 2/5 of Smith's weight. If the difference in their weight is 12kg, find John's weight?

2) Henry receives $4 more allowance than Gary a day. They spend $5 each per day. Henry saves twice as much as Gary a day. How much does Henry save in a day?

3) Jim used $600 of his salary on a TV Set. He spent 3/8 of the remaining salary on transport and the rest of it on food. If the amount spent on food is 1/4 of the total salary, what is the amount he spent on food?

Thanks

 

[stapel]

1) Pick variables for the weights. Write expressions for "one-sixth John's weight" and "two-fifths Smith's weight". Set the expressions equal; this is your first equation. Note that a smaller fraction of John's weight is equal to a larger fraction of Smith's weight. Deduce which weight is larger. Subtract the smaller from the larger, and set equal to the given difference. This is your second equation.

Solve the system of equations.

2) Pick a variable for the amount of Gary's allowance. Write an expression, in terms of this variable, for Henry's allowance. Write expressions for how much is left after their spending. Write an equation that stands for "Henry's savings are twice Gary's savings". Solve the equation for the value of the variable. Back-solve for the allowance amounts.

3) Pick a variable for the salary amount. Write an expression for the amount remaining after buying the television. Note that he has 5/8 of the rest after he pays for transportation, and that this remaining amount is equal to 1/4 of the original amount. Convert this equivalence into an equation, and solve. Back-solve for the amount he spent on food.

In future, please post algebra questions in one of the "algebra" categories, and please show some work. Thank you.

Eliz.