Math Word Problems Demystified - A Self Teaching Guide
LESSON 18 Solving Word Problems Using Two Equations If you need to review systems of equations, complete Refresher V. Many of th ...
In this lesson, a sample of each type of problem is solved by using a system of two equations with two unknowns. You will find t ...
2 x¼ 18 21 x 21 ¼ 18 2 x¼ 9 Find the other number. y¼xþ 8 y¼ 9 þ 8 y¼ 17 Hence, the numbers are 9 and 17. EVALUATION: Check the ...
Since reversing the digits gives a new number which is 9 more than the original number, the equation is ð 10 xþyÞþ 9 ¼ð 10 yþxÞ ...
7 7 þy¼ 15 7 y¼ 8 Hence, the number is 78. EVALUATION: Check the information in the second equation. Original number¼ 78 Rev ...
IMPLEMENTATION: Solve the system xþy¼ 8 25 xþ 10 y¼ 125 Find the value ofy in the first equation. Substitute it in the second eq ...
EVALUATION: Find the values of each and see if their sum is $1.25. 3 quarters¼ 3 $ 0 : 25 ¼$ 0 : 75 5 dimes¼ 5 $ 0 : 10 ¼$ 0 : ...
Substitute the value ofxin the second equation and solve forysince x¼yþ8. xþ 3 ¼ 2 ðyþ 3 Þ ðyþ 8 Þþ 3 ¼ 2 ðyþ 3 Þ yþ 8 þ 3 ¼ 2 y ...
SOLUTION: GOAL: You are being asked to find the distance the person walked to the stadium. STRATEGY: Letx¼the time the person wa ...
3 xþ 22 x¼ 44 22 xþ 22 x 25 x¼ 44 251 x 25 ¼ 44 25 x¼ 1 :76 hours Find the distance usingD¼RT. D¼RT D¼ 3 ð 1 : 76 Þ ¼ 5 :28 mi ...
Since the total amount of the mixture is 20 pounds, the first equation is xþy¼ 20 Since the cost of the mixture is $3.75, the se ...
Solve forx: xþy¼ 20 xþ 5 ¼ 20 xþ 5 5 ¼ 20 5 x¼15 pounds Hence, 15 pounds of the $4 coffee are needed and 5 pounds of the $3 ...
Since the total interest is $245, the second equation is 4%xþ 6 1 2 %y¼ 245 IMPLEMENTATION: Solve the system xþy¼ 5000 4%xþ 6 1 ...
Findx: xþy¼ 5000 xþ 1800 ¼ 5000 xþ 1800 1800 ¼ 5000 1800 x¼$ 3200 Hence, he has $3200 invested at 4% and $1800 invested at 6 ...
A person made 40 small bags of candy, some of which sold for $0.50 and the rest sold for $0.75 each. If the total amount he mad ...
Solve foryin the first equation. y¼ 14 x Substitute in the second equation and solve forx. 10 xþð 14 xÞþ 18 ¼ 10 ð 14 xÞþx 10 ...
Solve foryin the first equation. xxþy¼ 18 x y¼ 18 x Substitute in the second equation and solve forx. 5 xþ 10 ð 18 xÞ¼ 130 5 ...
Substitute forxin the second equation and solve fory. 4 yþ 10 ¼ 2 yþ 20 4 y 2 yþ 10 ¼ 2 y 2 yþ 20 2 yþ 10 ¼ 20 2 yþ 10 10 ¼ ...
Substitute in the second equation and solve forx. 50 xþ 75 ð 40 xÞ¼ 2325 50 xþ 3000 75 x¼ 2325 25 xþ 3000 ¼ 2325 25 xþ 30 ...
VI REFRESHER Quadratic Equations An equation such as 2x^2 þ 3 x 5 ¼0 is called aquadratic equation or a second-degree equation. ...
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