Difference between revisions of "2023 AMC 10A Problems/Problem 8"
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− | To solve this question, you can use y = mx + b where the x is the Fahrenheit and the y is the Breadus. We have (110,0) and (350,100). We want to find (200,y). The slope for these two points is 5/ | + | To solve this question, you can use <math>y = mx + b</math> where the <math>x</math> is the Fahrenheit and the <math>y</math> is the Breadus. We have <math>(110,0)</math> and <math>(350,100)</math>. We want to find <math>(200,y)</math>. The slope for these two points is <math>\frac{5}{12}</math>; <math>y = \frac{5}{12}x + b</math>. Solving for <math>b</math> using <math>(110, 0)</math>, <math>\frac{550}{12} = -b</math>. We get <math>b = \frac{-275}{6}</math>. Plugging in <math>(200, y), \frac{1000}{12}-\frac{550}{12}=y</math>. Simplifying, <math>\frac{450}{12} = \boxed{\textbf{(D) }37.5}</math> |
~walmartbrian | ~walmartbrian |
Revision as of 21:10, 9 November 2023
Contents
[hide]Problem
Barb the baker has developed a new temperature scale for her bakery called the Breadus scale, which is a linear function of the Fahrenheit scale. Bread rises at degrees Fahrenheit, which is degrees on the Breadus scale. Bread is baked at degrees Fahrenheit, which is degrees on the Breadus scale. Bread is done when its internal temperature is degrees Fahrenheit. What is this in degrees on the Breadus scale?
Solution 1
To solve this question, you can use where the is the Fahrenheit and the is the Breadus. We have and . We want to find . The slope for these two points is ; . Solving for using , . We get . Plugging in . Simplifying,
~walmartbrian
Solution 2 (faster)
Let denote degrees Breadus. We notice that is degrees to , and to . This ratio is ; therefore, will be of the way from to , which is
~Technodoggo
See Also
2023 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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