The Mendez family invested 5000 part at 3 and the remainder

The Mendez family invested $5000, part at 3% and the remainder at 3.5%. The annual income from both investments is $167. What is the amount invested at each rate? A dietician must plan a breakfast menu that provides 460 Cal, 9 g of fat, and 55 mg of calcium. One plain bagel contains 200 Cal, 2 g of fat, and 29 mg of calcium. A one-tablespoon serving of cream cheese contains 100 Cal, 10 g of fat, and 24 mg of calcium. One banana contains 105 Cal, 1 g of fat, and 7 g of calcium. (Source: Home and Garden Bulletin No. 72, U.S. Government Printing Office, Washington D.C. 20402) How many servings of each are required to provide the desired nutritional values? A student has a total of 225 on three tests. The sum of the scores on the first and second tests exceeds the score on the third test by 61. The first score exceeds the second by 6. Find the three scores.

Solution

23) Let x be the amount invested at 3% and y be the amount invested at 3.5%

Then x + y = 5000 =>y = 5000-x

(0.03)x + (0.35)(5000-x) = 167

=> 0.03x + 1750 - 0.35x = 167

=> -0.32x = 167-1750

=> -0.32x = -1583

=> x = 4946.875

And also y = 5000-4946.875 = 53.125

Hence he spend 4946.875 at 3% and 53.125 at 3.5%

25) Let the three scores be x, y and z

x + y + z = 225...(i)

x + y = z + 61...(ii)

x = y + 6...(iii)

(ii) subsituted in (i)

z+61 + z = 225

=> 2z = 225-61 = 164

=> z = 164/2 = 82

x + y = 82 + 61 = 143

x = y+6 => y+6 + y = 143

=> 2y = 143-6=137

=>y = 137/2 = 68.5

x = 68.5 + 6 = 74.5

Hence the scores on three tests are 74.5, 68.5 and 82