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Chapter 2: Problem 45

It takes six cups of flour to bake one cake; exactly one cup of flour has a mass of \(120.0 \mathrm{~g}\). If you have \(6955 \mathrm{~g}\) of flour, how many cakes can you bake? (Hint: Two conversion factors are given in this problem. Find them and write them down first in ratio form. Then use them in the correct form with the measured quantity, which is \(6955 \mathrm{~g}\) of flour.)

Short Answer

Expert verified
With 6955 g of flour, we can bake 9 cakes.

Step by step solution

01

Identify the conversion factors

The first conversion factor is the relationship between grams and cups: \(1 \: \text{cup} = 120.0 \: \text{g}\) The second conversion factor is the relationship between cups and cakes: \(1 \: \text{cake} = 6 \: \text{cups}\) Now we will use these conversion factors to convert the given mass of flour to the number of cakes.
02

Convert grams of flour to cups

Using the grams-to-cups conversion factor, we have: \(\frac{1 \: \text{cup}}{120.0 \: \text{g}}\) We will multiply this factor by the given mass of flour to convert it to cups: \(6955 \: \text{g} \times \frac{1 \: \text{cup}}{120.0 \: \text{g}}\) Dividing 6955 by 120 and calculating: \(\text{Number of cups} = \frac{6955}{120} = 57.9583 \: \text{cups}\)
03

Convert cups of flour to cakes

Next, we will use the cups-to-cakes conversion factor: \(\frac{1 \: \text{cake}}{6 \: \text{cups}}\) Multiply this factor by the number of cups obtained in the previous step: \(57.9583 \: \text{cups} \times \frac{1 \: \text{cake}}{6 \: \text{cups}}\) Dividing 57.9583 by 6 and calculating: \(\text{Number of cakes} = \frac{57.9583}{6} = 9.6597 \: \text{cakes}\) Since we cannot bake a fraction of a cake, we'll round this down to the nearest whole number:
04

Round down to the nearest whole number of cakes

The total number of cakes that can be baked with 6955 g of flour is: \(\text{Number of cakes} = \lfloor 9.6597 \rfloor = 9 \: \text{cakes}\) So, with 6955 g of flour, we can bake 9 cakes.

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