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# [Smart Math] Ratio Proportion Problem 56

Here’s and example of a SMART MATH problem for RATIO PROPORTION.

Three types of tea each worth $6.00 / lb,$7.50 / lb and $x / lb are mixed in proportion of 1 : 2 : 3 to form a mixture worth$8.50 / lb. What is the value of x in $/ lb? 1. 7.00 2. 7.50 3. 8.00 4. 8.50 5. 10.00 ### The Usual Method [contentblock id=google-adsense-post] Let the quantities of each type of$6.00, $7.50 and$x of tea be 1 lb, 2 lbs and 3 lbs respectively as per their proportions.

Hence total worth of tea = $6\times 1+7.5\times 2+x\times 3$

$=6+15+3x$

$=21+3x$

Hence cost / lb = $\frac{21+3x}{6}$

This is equal to $8.50 / lb $\therefore \frac{21+3x}{6}=8.50$ $\therefore 21+3x=8.5\times 6=51$ $\therefore 3x=30$ $\therefore x=10$ (Ans: 5) Estimated Time to arrive at the answer = 60 seconds. ### Using Technique [contentblock id=google-adsense-post] Observe that if two types of tea of$6 and $7.50 to be mixed with a third type of$x to form a mixture costing $8.50, the cost of the third type of tea should be more than$8.50. This means that you can eliminate all other options except ‘5’ i.e. \$10 which is the answer.

(Ans: 5)

Estimated Time to arrive at the answer = 5 seconds.
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