Lesson Entertainment problems on finding three unknowns using only one equation
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<H2>Entertainment problems on finding three unknowns using only one equation</H2> In joking form, this lesson teaches you to find three unknowns using only one single equation (for some problems, where such approach works). <H3>Problem 1</H3>A school cafeteria cashier has collected $243 in one-dollar, five-dollar, and ten-dollar bills. The number of one-dollar bills is eight more than 20 times the number of ten-dollar bills. The cashier also has seven more than twice the number of ten-dollar bills in five-dollar bills. How many bills of each value does the cashier have? <B>Solution</B> <pre> Let x be the number of the ten-dollar bills. Then the number of one-dollar bills is (8+20x) and the number of five-dollar bills is (7+2x). Now write the total money equation 243 = 10x + (8+20x) + 5*(7+2x). Simplify and find x 243 = 10x + 8 + 20x + 35 + 10x 243 = 40x + 43 40x = 243 - 43 40x = 200 x = 200/40 = 5 <U>ANSWER</U>. 5 ten-dollar bills; (8+20*5) = 108 one-dollar bills and (7+2*5) = 17 five-dollar bills. <U>CHECK</U>. 5*10 + 108*1 + 17*5 = 243 total money. ! Correct ! </pre> In joking form, this problem is about finding three unknown using only one equation . . . <H3>Problem 2</H3>You are at the store, and are trying to remember how much bread, meat, and cheese you were supposed to buy. The bread costs $3 per loaf, the meat costs $5 per pound, and the cheese costs $2 per pound. You know that you are to buy fifteen items, that the total cost will be $51, and that you are supposed to purchase one more meat than cheese. How many meat do you need to purchase? <B>Solution</B> <pre> x pounds of meat, (x-1) pounds of cheese and (15 - x - (x-1)) = 16-2x loaves of bread. The total money equation is 3*(16-2x) + 5x + 2*(x-1) = 51. (1) Simplify and find x 48 - 6x + 5x + 2x - 2 = 51 46 + x = 51 x = 51 - 46 <U>ANSWER</U>. 5 pounds of meat. <U>CHECK</U>. Then the left side of equation (1) is 3*(16-2*5) + 5*5 + 2*(5-1) = 51, which is precisely correct. </pre> My other additional lessons on solving single linear equations and word problems in one unknown in this site (section 2) are - <A HREF=https://www.algebra.com/algebra/homework/equations/One-more-lesson-on-solving-problems-by-the-backward-method.lesson>One more lesson on solving problems by the backward method</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Choose-an-unknown-variable-in-a-rational-way-for-your-problem.lesson>Choose an unknown variable in a rational way for your problem</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/Upper-level-word-problems-to-solve-using-single-linear-equation.lesson>Upper level word problems to solve using a single linear equation</A> - <A HREF=https://www.algebra.com/algebra/homework/equations/OVERVIEW-of-my-additional-lessons-on-solving-single-linear-equations-and-word-problems-in-one-unknown.lesson>OVERVIEW of my additional lessons on solving single linear equations and word problems in one unknown</A>
