Answer:
<h2>a = 5 cm, b = 2 cm.</h2>
Step-by-step explanation:
![\text{We have:}\\\\A_{PQRS}=45\ cm^2\\\\A_{PQRS}=a(7+b)\\\\A_{PXYS}=10\ cm^2\\\\A_{PXYS}=ab\\\\\text{Therefore we have the system of equations:}\\\\\left\{\begin{array}{ccc}a(7+b)=45&\text{use the distributive property}\\ab=10\end{array}\right\\\left\{\begin{array}{ccc}7a+ab=45&(1)\\ab=10&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\7a+10=45\qquad\text{subtract 10 from both sides}\\7a=35\qquad\text{divide both sides by 7}\\a=5\\\text{Put it to (2):}\\5b=10\qquad\text{divide both sides by 5}\\b=2](https://tex.z-dn.net/?f=%5Ctext%7BWe%20have%3A%7D%5C%5C%5C%5CA_%7BPQRS%7D%3D45%5C%20cm%5E2%5C%5C%5C%5CA_%7BPQRS%7D%3Da%287%2Bb%29%5C%5C%5C%5CA_%7BPXYS%7D%3D10%5C%20cm%5E2%5C%5C%5C%5CA_%7BPXYS%7D%3Dab%5C%5C%5C%5C%5Ctext%7BTherefore%20we%20have%20the%20system%20of%20equations%3A%7D%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Da%287%2Bb%29%3D45%26%5Ctext%7Buse%20the%20distributive%20property%7D%5C%5Cab%3D10%5Cend%7Barray%7D%5Cright%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D7a%2Bab%3D45%26%281%29%5C%5Cab%3D10%26%282%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7BSubstitute%20%282%29%20to%20%281%29%3A%7D%5C%5C7a%2B10%3D45%5Cqquad%5Ctext%7Bsubtract%2010%20from%20both%20sides%7D%5C%5C7a%3D35%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%207%7D%5C%5Ca%3D5%5C%5C%5Ctext%7BPut%20it%20to%20%282%29%3A%7D%5C%5C5b%3D10%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%205%7D%5C%5Cb%3D2)
Answer:
To solve for the problem above, let x be the regular price of the shoe.
1/2x is the one-half price of the shoe then we add 6 for the pair of socks,
1/2x + 6, then lola has 32 left so we add that too, 1/2x + 6 + 32 = 75. The total amount of lola spent is 75 - 32, which is 1/2x + 6.