# Lesson 124 of Doodles Do Algebra

Today’s exercise is to learn to recognize and translate a word problem into 3 independent equations with 3 unknowns, or 4 equations and 3 unknowns. As a bonus, and for practice your child gets to pick one of the two problems and solve it all the way after writing down the equations.

1. First equation: $x+y+z=59$

Second equation: $y-x=5$

Third equation: $z-x=9$

Solution: rewrite second equation in terms of y equals something and the third equation in terms of z equals something. Then plus those both into the first equation and solve for x. Then plug that value of x into the second equation to solve for y and into the third equation to solve for z and you are done.

2.

First equation: $2r+5c=12$ where r is price of one roll and c is price of one cookie.

Second equation: $3c+5l=18$ where c is price of one cookie and l is price of one loaf of bread.

Third equation: $4c+5p=28$ where c is price of one cookie and p is price of one pretzel.

Fourth equation: $5l+6p=?$

Since I did not include the cost of the final trip to the store, you do not have 4 independent equations and 4 unknowns, only 3 equations and 4 unknowns. This is not a solvable problem, so if your child points that out then give her a gold star and lots of praise!