MATH SOLVE

3 months ago

Q:
# Ronald received a special toy train set for his birthday. In the picture of the train on the package, the boxcar has the following dimensions: length is 4 5/16 inches; width is 1 1/8 inches; and height is 1 5/8 inches. The toy boxcar that Ronald received has dimensions l is 17.25 inches; w is 4.5 inches; and h is 6.5 inches. If the actual boxcar is 50 feet long:a. Find the scale factor of the picture on the package to the toy set.b. Find the scale factor of the picture on the package to the actual boxcar.c. Use these two scale factors to find the scale factor between the toy set and the actual boxcar.d. What are the width and height of the actual boxcar?

Accepted Solution

A:

Answer:a. 4b. 3200/23c. 800/23d. height 18 58/69 ft width 13 1/23 ftStep-by-step explanation:It is a long one, but an easy one!a. The scale factor of the picture on the package to the toy set is found by dividing any of the measures of the toy by the measures of the picture. In this case, let's divide the length:Length of the toy set 17.25 inches, which is 17 1/4 inches, Length of the picture 4 5/16:[tex]\frac{17\frac{1}{4}}{4\frac{5}{16} }=\frac{\frac{69}{4} }{\frac{69}{16} }=\frac{16}{4} =4[/tex]so the scale factor is 4b. We already know that multiplying the length by 4 equals the length of the toy. Now We divide the length of the actual boxcar by the length of the picture to find the scale factor.Length of the boxcar 50 feet, one foot has 12 inches, so the length of the boxcar multiplied by 12 is the length in inches.50 feet [tex](\frac{12"}{1ft} )= 600"[/tex]Length of the boxcar 600"Length of the picture 4 5/16"[tex]\frac{\frac{600}{1} }{4\frac{5}{16} }=\frac{\frac{600}{1} }{\frac{69}{16} }= \frac{600*16}{69} =\frac{600*16}{23*3} =\frac{200*16}{23} =\frac{3200}{23}[/tex]so the scale factor for the picture on the package to the actual boxcar is 3200/23c. We divide the scale factor of the picture to the actual boxcar by the factor of the picture to the toy set. And we get[tex]\frac{\frac{3200}{23} }{\frac{4}{1} }= \frac{800}{23}[/tex]The scale factor between the toy set and the boxcar ir 800/23d. We multiply the height and the width of the toy by 800/23,that is,height[tex]6\frac{1}{2}*\frac{800}{23} =\frac{13}{2}*\frac{800}{23} = \frac{400*13}{23} =\frac{5200}{23}[/tex]Those are inches. To see them in feet we divide by 12.[tex]\frac{5200}{23} *\frac{1ft}{12"} =\frac{13*4*100}{23*4*3} =\frac{1300}{69}[/tex]1300/69 is equal to 18 multiplied by 69 and 58 left, which we can write as:[tex]\frac{1300}{69}ft =18\frac{58}{69} ft[/tex]Let's do the same with width[tex]4\frac{1}{2}*\frac{800}{23} =\frac{9}{2}*\frac{800}{23} =\frac{3600}{23} inches[/tex][tex]\frac{3600}{23}inches*\frac{1ft}{12 inches} =\frac{12*3*100}{23*12} =\frac{300}{23} ft[/tex]300/23 ft is 13 1/23 ft.