For the first Part A and Part B about Michelle’s house, the park, school, and grocery store, I don’t have enough information about the map to solve. Is there a diagram/illustration meant to go with those questions?
PART A: Jayesh creating an incorrect equation for the car. In an equation showing the relationship between distance and time, variable x represents time in hours and y is distance in miles. Given 180 miles (dist.) was travelled in 3 hours (time), x = 3 and y = 180.
We can find the car’s constant speed in miles per hour (mph) by dividing the distance by time: 180mi/3h = 60mph.
In Jayesh’s equation, they incorrectly solve for x, the time. They wrote 60y = x. If we plug in the given values, then 60(180) = 3. This is NOT true as 10,800 ≠ 3.
The correct equation is going to find the distance travelled, y, using the speed and time, x. Try 60x = y. This is similar to Jayesh’s equation but the variables swap places. We want to solve for the distance, y, and NOT the time, x, like Jayesh tried to do. Plug in given values: 60(3) = 180 becomes 180 = 180 which is true on both sides of the equation.
ANSWER to PART A: 60x = y
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PART B: write a truck equation. Given 150 miles travelled in 3 hours, y = 150 and x = 3.
Using what we did above in Part A, we can set up an equation after finding the constant speed of the truck. 150mi/3h = 50mph.
Try 50x = y. Plug in given values and 50(3) = 150 becomes 150 = 150 which is true!!
ANSWER to PART B: 50x = y.
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PHONE MAP QUESTION: given a width of 1.2 inches on the phone map equals 400ft if the park’s actual distance, we can find the Scale Factor.
1.2in/400ft = 0.003. The scale factor means that each 0.003 inches in his phone represents one foot of the actual park distance. Check: 400ft*0.003=1.2in -> 1.2 = 1.2 (true!).
So, when the actual distance is 300 feet, we can use the Scale Factor, 0.003, to calculate the length of the park on his phone map.
300ft*0.003 = 0.9 inches
ANSWER: 0.9 inches.
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QUESTION 4: Circular fountains. Architect’s scale factor enlarges radius 1:4. Area of Architect’s fountain is 1,600(pi) square yards.
The architect took the versailles‘s fountain radius and multiplied it by 4, according to the scale factor he used, 1:4. The area of a circle is given by A=(pi)r^2
40^2 = 1,600 so the architects NY fountain radius must be 40 yards. Dividing that by the scale factor of 4 will find the versailles‘s fountain radius: 40/4 = 10.
The palace of Versailles‘s fountain has a radius of 10 yards. Given A=(pi)r^2,
A=(pi)(10yd)^2
A=(pi)100sq. yds
ANSWER to Q4: 100(pi) square yards.
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QUESTION 7: Jamie & Mia. Jamie uses the sales tax before the coupon. Mia thinks using the coupon before the sales tax will result in a lower total. Why is she incorrect?
Given:
Total cost (before tax) = $24.00
Coupon = 25% off
Sales tax = 8%
To start, 25%=0.25 as a decimal and 8%=0.08.
Jamie’s way: 24.00*0.08=1.92
24.00+1.92=25.92.
$25.92 is the total after tax.
Now 25% off that: 25.92*0.25=6.48.
Subtract $6.48 from the total.
$25.92 - $6.48 = $19.44.
Jamie’s method calculated a total of $19.44 after tax and applying the coupon.
Mia’s way: 24.00*0.25=6.
Subtract $6.00 from the total.
24.00-6.00 = 18.00.
After applying the coupon, the total is $18.00. Now 8% sales tax added to that: 18.00*0.08=1.44.
$18.00 + $1.44 = $19.44.
Mia‘s method results in the same total of $19.44 after applying the coupon before the sales tax.
Mia will not calculate a lower total for using the coupon first. Jamie and Mia‘s order of operations result in the same total cost of $19.44.