Three Algebra Word Problems on Simultaneous Linear Equations

1. At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for $1.25. What was the price of a book and what was the price of a magazine?

2. Ziggy's Famous Yogurt blends regular yogurt that is 3% fat with its no-fat yogurt to obtain lowfat yogurt that is 1% fat. How many pounds of regular yogurt and how many pounds of no-fat yogurt should be mixed to obtain 60 pounds of low-fat yogurt?

3. The probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Super Bowl. The probability that San Francisco plays in the next Super Bowl plus the probability that they do not play is 1. What is the probability that San Francisco plays in the next Super Bowl?

Solution Preview

72. Let the price of a book be x and the price of a magazine be y.
Then according to Harriet, 4x+3y =1.45 [1]
And, according to June, 2x+5y = ...

Solution Summary

This solution sets up and solves the three word problems using systems of equations.

For solving a system of equations, is there a difference between using an algebraic method and using the graphical method? Explain why or why not, and include a numerical example to illustrate your point.

Bottle A contains an 80% acid solution. Bottle B contains a 20% solution of the same acid. How many cc from bottle B should be mixed with solution from bottle A to make 40 cc of a mixture which is 40% acid?

3. (a) Solve the following systems of equations
i)
x + 2 y - z = 2
-3 x - y + z = -3
- x+ 3 y - z = 1
ii)
4 x+ -3 y+ z = - 1
-3 x+ y+ -5 z = 0
-5 x -4 z = 0
iii)
x1 + x2 + x3 = 3
-3 x1 -17 x2 + x3 + 2 x 4 = 1
4 x -7 x2 + 8 x3 -5 x4 = 1
-5 x2 -2 x3 + x4 = 1
(b) Find the values of k for which

Solve the simultaneouslinearequations by using the following methods
a) substitution method
b) Algebraic Elimination Method
c) Cramer's Rule method
2x-3y= 5
3x+7y= -2
Please show all work.

1. The surface area S of a right prism is given by S = 2B + Ph.
B is the area of the base.
P is the perimeter of the base.
And h is the height of the prism. Solve for B.
2. The length of a rectangle is five times its width. If the area of the rectangle is 500m², find its perimeter.
3. The sum of two numbers is grea

With referrence to the last solutions u posted to me,may you please check no 1 I have a different solution from my workings.I not sure which one is correct,but I think mine might be.If so may u please edit the document because I failed to do so.I will use this over and over.

A landscaper wants to combine golden landscape rock with rust-colored landscape rock to make a mix. The golden rock costs $0.59 per pound and the rust-colored rock cost $0.49 per pound. If the landscaper buys 70 pounds of the mixture costing a total of $38.80, how much of the rust-colored rock did he buy?
___Pounds