Question - Solving Model Car Collection Ratios
Solution:
The question provided in the image states that Ahmadi has a total of 264 model cars in his collection, which he keeps in three different cabinets labeled X, Y, and Z. The ratio of the number of model cars in each cabinet is 2:3:1.We need to answer the following questions:a) Calculate the number of model cars in cabinet X to the nearest ten.b) $$ \frac{1}{4} $$ of the collection in cabinet Y is moved to cabinet Z. What is the number of model cars in cabinet Z to the nearest seven?c) Give the updated ratio of the number of model cars located in cabinets X, Y, and Z.Let's start solving them one by one:a) We have a ratio of 2:3:1, which adds up to 6 parts in total. Since we have 264 cars, each part represents $$ \frac{264}{6} = 44 $$ cars.For cabinet X, which represents 2 parts, we have $$ 44 \times 2 = 88 $$ cars. To round this to the nearest ten, we don't need to round at all because 88 is a multiple of ten.b) Cabinet Y has 3 parts, so it initially contains $$ 44 \times 3 = 132 $$ cars. We take $$ \frac{1}{4} $$ of these cars and move them to cabinet Z, which is $$ \frac{1}{4} \times 132 = 33 $$ cars.Cabinet Z initially has 1 part (44 cars), so after adding 33 cars from cabinet Y, cabinet Z will have $$ 44 + 33 = 77 $$ cars. To round this to the nearest seven, we find the multiple of 7 closest to 77, which is 77 itself (11x7=77).c) After moving $$ \frac{1}{4} $$ of cabinet Y's cars to Z, cabinet Y has $$ 132 - 33 = 99 $$ cars left.So the new ratio for cabinets X, Y, and Z, with the numbers of cars being 88, 99, and 77 respectively, does not simplify nicely into whole numbers. However, we can see that they are all divisible by 11:- X: $$ \frac{88}{11} = 8 $$- Y: $$ \frac{99}{11} = 9 $$- Z: $$ \frac{77}{11} = 7 $$Hence, the updated ratio of the model cars in cabinets X, Y, and Z is 8:9:7.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com