Answer:
Part A:
![4 + x = y](https://img.qammunity.org/2021/formulas/mathematics/middle-school/j61r867x1kha75b2ct58kh5azx2babh4pt.png)
![0.5*4 + 1*x = 0.7*y](https://img.qammunity.org/2021/formulas/mathematics/middle-school/t2k7e31jx0sil56ma1dcpvxiif7yo1i41j.png)
![x = 8/3\ quarts\ of\ 100\%\ solution](https://img.qammunity.org/2021/formulas/mathematics/middle-school/xmlrv2uicgkd4kib480pk2d9mbgwvp4lrr.png)
![y = 20/3\ quarts\ of\ 70\%\ solution](https://img.qammunity.org/2021/formulas/mathematics/middle-school/42jdmi30owoffo5akv9lv6jcbocx0eu7mk.png)
Part B:
![x + y = 10](https://img.qammunity.org/2021/formulas/mathematics/middle-school/8wt42z1z2h8g91o4g8azsrkg9i01hn4lbx.png)
![2x + 3y = 23](https://img.qammunity.org/2021/formulas/mathematics/middle-school/xjehn23hnxq3zrz1zy71ffhreeebt6ftpf.png)
and
![y = 3](https://img.qammunity.org/2021/formulas/mathematics/middle-school/acoo9469po7wyuqrdt46fqzahwmx3ebgvr.png)
Explanation:
Part A:
The inicial concentration of the lemonade is 50%, and the volume is 4 quarts, and we will add x quarts of a lemonade with a concentration of 100%, so the total volume will be y, and the concentration will be 0.7, so we have that:
![4 + x = y](https://img.qammunity.org/2021/formulas/mathematics/middle-school/j61r867x1kha75b2ct58kh5azx2babh4pt.png)
![0.5*4 + 1*x = 0.7*y](https://img.qammunity.org/2021/formulas/mathematics/middle-school/t2k7e31jx0sil56ma1dcpvxiif7yo1i41j.png)
Using the value of y from the first equation in the second one, we have:
![2 + x = 0.7*(4 + x)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/rshgedr8n9e130xp0tk21uyihwthfas4fl.png)
![2 + x = 2.8 + 0.7x](https://img.qammunity.org/2021/formulas/mathematics/middle-school/qfr84mgyprmh27x8w710gf1339y7a2149e.png)
![0.3x = 0.8](https://img.qammunity.org/2021/formulas/mathematics/middle-school/bdfet6z75sp7tuxduhb7y7g8itjxf6wvg3.png)
![x = 8/3\ quarts](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ru6d1n7owu9wioszsjyxf4aog5zv6ypi7o.png)
![y = 4 + 8/3 = 20/3\ quarts](https://img.qammunity.org/2021/formulas/mathematics/middle-school/v2en41551uzs09anot0n0nnrhkngwzrzd8.png)
Part B:
If he shoots a total of ten targets, we can write the equation:
![x + y = 10](https://img.qammunity.org/2021/formulas/mathematics/middle-school/8wt42z1z2h8g91o4g8azsrkg9i01hn4lbx.png)
Each stationary target is 2 points, and each moving target is 3 points, so if the total points is 23, we have:
![2x + 3y = 23](https://img.qammunity.org/2021/formulas/mathematics/middle-school/xjehn23hnxq3zrz1zy71ffhreeebt6ftpf.png)
If we subtract the second equation by two times the first one, we have:
![2x + 3y - 2*(x + y) = 23 - 2*10](https://img.qammunity.org/2021/formulas/mathematics/middle-school/w2m17oxteuggbqrf5ogacstacjzj7map3k.png)
![2x + 3y - 2x - 2y = 23 - 20](https://img.qammunity.org/2021/formulas/mathematics/middle-school/5qcypez08x41jlktsw8jipqiy0shtdk1yq.png)
![y = 3](https://img.qammunity.org/2021/formulas/mathematics/middle-school/acoo9469po7wyuqrdt46fqzahwmx3ebgvr.png)
⇒
![x = 7](https://img.qammunity.org/2021/formulas/mathematics/middle-school/haui06dyzu06cccqprdnwfvnybjm6zc7di.png)