Hi I need help figuring out these to word problems.
Tom has created a scale drawing of his property for use in designing a landscape plan. 1 in on is drawing corresponds to 12 ft. There is a pond that is 112 ft. long on his property. How long will it appear on the drawing? Round your answer to the nearest 0.5 in
Suppose that Barry Bonds has 148 hits in 500 at bats. How many hits does he need in his next 10 at bats to raise his batting average to .300?
Let's set up a proportion, cross multiply and solve for x.
1/12 = x/112
12x = 112
x = 9.33 = 9.5 inches
0.3 * 500 = 150
I understand the first concept, but I can't make out how you figured out the second word problem. How did you get 0.3?
batting average is a per 1000. So 356 is really an average of .356
I think the problem states the next 10 at bats so 0.3 x 510 = 153 hits needed. He already has 148 so he needs 5 more hits in his next 10 at bats. Or did I miss something?
Suppose that Barry Bonds has 148 hits in 500 at bats. How many hits does he need in his next 10 at bats to raise his batting average to .300?
Sure! Let's tackle the first word problem first:
Tom has created a scale drawing of his property where 1 inch on the drawing corresponds to 12 feet in real life. He wants to know how long the pond on his property will appear on the drawing.
To solve this problem, we can set up a proportion:
1 inch (on the drawing) / 12 feet (in real life) = x inches (on the drawing) / 112 feet (in real life)
To find "x", we can cross-multiply and solve for it:
1 inch * 112 feet = 12 feet * x inches
112 inches = 12x
x = 112 inches / 12
x = 9.33 inches
But we need to round the answer to the nearest 0.5 inches as specified in the question. Since 9.33 is closer to 9.5 than 9, the length of the pond will appear as 9.5 inches on the drawing.
Now let's move on to the second word problem:
Barry Bonds has 148 hits in 500 at bats and wants to know how many hits he needs in his next 10 at bats to raise his batting average to .300.
To solve this problem, we can use the formula for batting average:
Batting Average = Total Hits / Total At Bats
Barry Bonds' current batting average is 148 hits / 500 at bats, which can be simplified to 0.296.
To raise his batting average to 0.300, we can set up the following equation:
(148 hits + x hits) / (500 at bats + 10 at bats) = 0.300
To solve for "x" (the number of hits he needs in his next 10 at bats), we can cross-multiply and solve for it:
(148 + x) / (500 + 10) = 0.300
(148 + x) / 510 = 0.300
Cross-multiplying gives us:
0.300 * 510 = 148 + x
153 = 148 + x
Subtracting 148 from both sides:
153 - 148 = x
5 = x
So, Barry Bonds needs 5 hits in his next 10 at bats to raise his batting average to .300.
I hope this explanation was helpful! Let me know if you have any further questions.