STEP1) READ THE QUESTION AND CHOOSE BETWEEN VENN DIAGRAM AND DOUBLE MATRIX. I DID THIS QUESTION BOTH WAYS AND FOUND THAT VENN DIAGRAM IS EASIER. IF ANYONE HAS A WAY TO QUICKLY DISCERN THE EASIEST WAY TO SOLVE THIS QUESTION LET ME KNOW. I DON'T I WAS QUICK ENOUGH TO CHOOSE VENN DIAGRAM FOR THIS QUESTION BUT I WANT TO GET BETTER AT DISCERNING BETWEEN THE TWO (VENN DIAGRAM VS. DOUBLE MATRIX)

STEP2) IDENTIFY FOR WHICH VARIABLE YOU WILL BE SOLVING. THIS QUESTION ASKS FOR FRENCH WHICH I HAVE LABELED "C". THIS IS IMPORTANT BECAUSE AT THE VERY END OF THE SOLUTION I MUST DOUBLE CHECK THAT MY ANSWER IS FOR C AND NOT FOR OTHER VARIABLE.

STEP3) TRANSLATE INTO FORMULAS

FORMULA 1) A+B+C+D=200

FORMULA 2) B=D

FORMULA 3) 1/4(A+B)=B =>HERE SIMPLIFY TO A=3B. AT THIS POINT YOU SHOULD REALIZE THAT YOU HAVE D AND A IN TERMS OF B, YOU ONLY NEED C TO BE IN TERMS OF B IN ORDER TO GO BACK TO FIRST FORMULA AND SOLVE.

FORMULA 4) B+C=A-10 => REPLACE A WITH A=3B => B+C=3B-10 => C=2B-10

STEP4) REPLACE TO THE FORMULA 1) NOW THAT ALL THE FORMULAS ARE IN TERMS OF B.

A+B+C+D=200 => 3B+B+2B-10+B=200 => B=30

STEP5) SOLVE FOR C IN THE FORMULA, C=2B-10 => C=2(30)-10 => 60-10 => C=50

Attachments

image1 (2).JPG [ 364.48 KiB | Viewed 1992 times ]