Answer:
1. Daniel has 24 local stamps.
2. Mr. Kim cut the shorter piece of wire to 30 cm.
3. The volume of the green paint is 1050 milliliters.
5. The ratio of the tv price to the table price is 24:11
6. The ratio of the cards Chris gave away to the ones he has left is 3:8
7. There are 704 passengers in total.
Step-by-step explanation:
1. The total number of stamps is 96 and the ratio is 1:3. If you add the 1+3 to get a total, you get 4. For every 4 stamps, 1 is local and 3 are foreign. If you divide 96 by 4, you get 24. Since the ratio is only 1:3, the ratio is 24:72. (to get the 72, just divide 24*3[the other ratio number]) To check it, you can divide each side by 24 and you'll end up with the original ratio.
2. If the wire in total is 180 cm, you can do the same you did with number 1. Add the ratio to make it a total, 1:5 - 1+5 =6 then divide 180 by 6. 180/6 is 30. Multiply your quotient with the ratios and you'll get the full ratio. The ratio ends up being 30: 150 and if you add them, you do get 180 which is the length of the wire :)
3: The ratio of this is 3:4 of blue paint to yellow paint. You get the information that 600 milliliters of yellow paint is used. With that, you can create the equation 3/4 = x/600. You get x/600 because the amount of blue paint is unknown therefore you use an x for that ratio. To solve that, you multiply diagonally and get 1800/4x. If you divide it you get 450x. Basically, 450 is the amount of blue paint and if you add it with the yellow paint, you get 1050 milliliters of the green paint that had been created.
5. The table costs $275 and the TV is $325 more than the table. If you add them, you get the cost of the TV, which is $600. The ratio of the price of the TV to the table is 600:275. Once you simplify it, it's 24:11. To simplify it, divide it by the GCF and in this case, the GCF is 25.
6. Chris starts with 198 cards but gives 54 away. He ends up with 144. The ratio is 54:144 because it is a ratio of how many he gave away to how many he has left. Once you simplify the ratio, it's 3:8.
7. There are 288 seated passengers and the ratio of seated passengers to standing passengers is 9:13. In this problem, you make an equation, 288/x = 9/13. You multiply diagonally, 288*13 = 3744 and 9x. you end up with 3744/9x and when you divide it, you get 416. 416 represents the number of standing passengers. If you add 416 and 288, you get the number of total passengers which is 704.
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