QuestionCalculate ingredient amounts for 50 meatballs and compare beef prices at two shops. Verify age-based R3600 distribution for three kids. Analyze number patterns A and B.

Studdy Solution

STEP 1

Assumptions1. The recipe serves4 people with the following ingredients - $500 \mathrm{~g}$ lean minced beef -1 egg - teaspoons dried mixed herbs - $50 \mathrm{~ml}$ cooking oil - $400 \mathrm{~g}$ canned chopped tomatoes - $250 \mathrm{~g}$ fresh egg noodles. Josh wants to make meatballs for50 people.
3. The original recipe produces20 meatballs which serve4 people.
4. Shop A offers $\mathrm{~kg}$ for R250, whereas Shop B provides $3 \mathrm{~kg}$ for R315.
5. Mr Smith has three children aged3 years,5 years and10 years. R3600 has been set aside which is to be shared proportionally according to age.
6. The number patterns are given as - A= $\{27 ;25 ;23 ;21 ;19 ;-;-;-\}$ - B= $\{9 ;18 ;36 ;72 ;-;-;-\}$

STEP 2

First, we need to calculate the amount of minced beef and canned chopped tomatoes Josh needs. We can do this by multiplying the amount needed for4 people by the ratio of50 to4.
$Amount\, for\,50\, people = Amount\, for\,4\, people \times \frac{50}{4}$

STEP 3

Now, plug in the given values for the minced beef and canned chopped tomatoes to calculate the amount needed for50 people.
$Minced\, beef\, for\,50\, people =500 \mathrm{~g} \times \frac{50}{}$ $Canned\, tomatoes\, for\,50\, people =400 \mathrm{~g} \times \frac{50}{}$

STEP 4

Calculate the amount of minced beef and canned chopped tomatoes needed for50 people.
$Minced\, beef\, for\,50\, people =500 \mathrm{~g} \times \frac{50}{4} =6250 \mathrm{~g}$ $Canned\, tomatoes\, for\,50\, people =400 \mathrm{~g} \times \frac{50}{4} =5000 \mathrm{~g}$

STEP 5

Next, we need to calculate the number of eggs needed. Since the recipe for4 people requires1 egg, the recipe for50 people will require the number of eggs to be multiplied by the ratio of50 to4.
$ggs\, for\,50\, people =1 \times \frac{50}{4}$

STEP 6

Calculate the number of eggs needed for50 people.
$ggs\, for\,50\, people =1 \times \frac{50}{4} =12.5$ Since we can't have half an egg, Josh will need13 eggs.

STEP 7

Next, we need to compare the prices of lean minced beef at Shop A and Shop B. We can do this by calculating the price per kilogram at each shop.
$Price\, per\, kg\, at\, Shop\, A = \frac{R250}{2 \mathrm{~kg}}$ $Price\, per\, kg\, at\, Shop\, B = \frac{R315}{3 \mathrm{~kg}}$

STEP 8

Calculate the price per kilogram at each shop.
$Price\, per\, kg\, at\, Shop\, A = \frac{R250}{2 \mathrm{~kg}} = R125 \mathrm{~per~kg}$ $Price\, per\, kg\, at\, Shop\, B = \frac{R315}{3 \mathrm{~kg}} = R105 \mathrm{~per~kg}$ Therefore, Shop B sells minced meat cheaper per kilogram.

STEP 9

Next, we need to calculate the number of meatballs needed to serve24 and30 people. We can do this by multiplying the number of meatballs for4 people by the ratio of the number of people to4.
$Meatballs\, for\,24\, people =20 \times \frac{24}{4}$ $Meatballs\, for\,30\, people =20 \times \frac{30}{4}$

STEP 10

Calculate the number of meatballs needed for24 and30 people.
$Meatballs\, for\,24\, people =20 \times \frac{24}{4} =120$ $Meatballs\, for\,30\, people =20 \times \frac{30}{4} =150$

STEP 11

Next, we need to calculate how much each of Mr Smith's children will receive from the R3600. We can do this by dividing the total amount by the sum of the children's ages and then multiplying by each child's age.
$Amount\, for\,3\, year\, old = R3600 \times \frac{3}{(3+5+10)}$ $Amount\, for\,5\, year\, old = R3600 \times \frac{5}{(3+5+10)}$ $Amount\, for\,10\, year\, old = R3600 \times \frac{10}{(3+5+10)}$

STEP 12

Calculate the amount each child will receive.
$Amount\, for\,\, year\, old = R3600 \times \frac{}{18} = R600$ $Amount\, for\,5\, year\, old = R3600 \times \frac{5}{18} = R1000$ $Amount\, for\,10\, year\, old = R3600 \times \frac{10}{18} = R2000$ Therefore, the eldest child's claim is incorrect. He will receive R2000, not R1800.

STEP 13

Next, we need to classify the number patterns A and B as Geometric or Numeric (linear) patterns.A Numeric (linear) pattern is one where each term is a fixed amount more or less than the previous term.A Geometric pattern is one where each term is a fixed multiple of the previous term.
Looking at pattern A, each term is2 less than the previous term, so it is a Numeric (linear) pattern.
Looking at pattern B, each term is twice the previous term, so it is a Geometric pattern.

STEP 14

Finally, we need to find the next two terms for each pattern.
For pattern A, since each term is2 less than the previous term, the next two terms will be17 and.
For pattern B, since each term is twice the previous term, the next two terms will be144 and288.

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