Geography tests

On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?

Correct answer:

p =  97.2 %

Step-by-step explanation:

$$\begin{gathered} e_1=150\cdot {\displaystyle \frac{88}{100}}=132 \\ {e}_2=150\cdot {\displaystyle \frac{94}{100}}=141 \\ {e}_3=150\cdot {\displaystyle \frac{90}{100}}=135 \\ {\displaystyle \frac{p}{100}}\cdot 250+e_1+e_2+e_3={\displaystyle \frac{93}{100}}\cdot (3\cdot 150+250) \\ b={\displaystyle \frac{93}{100}}\cdot (3\cdot 150+250)-e_1-e_2-e_3={\displaystyle \frac{93}{100}}\cdot (3\cdot 150+250)-132-141-135=243 \\ p=100\cdot {\displaystyle \frac{b}{250}}=100\cdot {\displaystyle \frac{243}{250}}={\displaystyle \frac{486}{5}}\mathrm{\%}=97.2\mathrm{\%} \end{gathered}$$

Try another example

Related math problems and questions:

• Test scores
  Jo's test scores on the first four 100 point exams are as follows: 96,90,76, and 88. If all exams are worth the same percent, what is the minimum test score necessary on his last exam to earn an A grade in the class (90% or better)?
• Statistics
  The sum of all deviations from the arithmetic mean of the numerical sequence 4, 6, 51, 77, 90, 93, 95, 109, 113, 117 is:
• Test points
  If you earned 80% of the possible 40 points, how many points did you miss to get 100%?
• Language test
  Your language test scores are 58, 68, 89 and 95. What is the lowest you can earn on the next test and still achieve an average of at least 79?
• Annual income
  The annual income (in thousands of $) of fifteen families is 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200. Calculate the harmonic and geometric mean.
• Percentages
  52 is what percent of 93?
• Four numbers
  The first number is 50% second, the second number is 40% third, the third number is 20% of the fourth. The sum is 396. What are the numbers?
• Acid solution
  By adding 250 grams of a 96% sulfuric acid solution to its 3% solution, we changed its initial concentration to 25%. How many grams of 3% of the acid was used for dilution?
• Final exam
  There are 5 learners in a class that has written a final exam Aleta scored 55% vera scored 36% and Sibusiso scored 88% if Thoko scored 71% and the class average was 63%. What was Davids score as a percentage?
• Pine
  How much of a mixed forest rangers want to cut down, if their head said: "We only cut down pine trees, which in our mixed forest 98%. After cut pine trees constitute 94% of all trees left."
• Profits
  Two members will make profit 52 000, - EUR. The forst earned 8% more and the second 10% more and thus earned together 56 700, - EUR. How many will initially each earn?
• Sisters
  Sisters Zuzka Lenka and Vierka has save for a new bike. Zuzka save € 90, Lenka save € 90 and Vierka save € 82. Missing 30% gave them their mother. What is the price of the bike?
• On a farm
  On a farm, there are 90 rabbits, 700 sheep, 300 cattle and 500 pigs. What percentage of the total number of animals are rabbits?
• Remainders
  It is given a set of numbers { 170; 244; 299; 333; 351; 391; 423; 644 }. Divide this numbers by number 66 and determine set of remainders. As result write sum of this remainders.
• Grams
  How many grams of 5% solution do we need to add to 100g of 50% solution to get a 20% solution?
• Adding percentages
  55%+36%+88%+71%+100=63% what is whole (X)? Percents can be added directly together if they are taken from the same whole, which means they have the same base amount. .. . You would add the two percentages to find the total amount.
• Percentages above 100%
  What is 122% of 185? What is the meaning of percentages above 100%?