Answer:
50 hammers and 20 wrenches.
Explanation:
Let x represent number of hammers and y represent number of ranchers.
We have been given that a store sold 70 hammers and ranchers. We can represent this information in an equation as:
![x+y=70...(1)](https://img.qammunity.org/2021/formulas/mathematics/high-school/88v526grymqttjvmkvzmv0q91x6ipfqv8g.png)
We are also told that each hammer sold for $10 and each rancher sold for five dollars resulting a total of 600.00. We can represent this information in an equation as:
![10x+5y=600...(2)](https://img.qammunity.org/2021/formulas/mathematics/high-school/9x88n8io78sx5xqcjx6bzv9szhyuuvt2eh.png)
From equation (1), we will get:
![x=70-y](https://img.qammunity.org/2021/formulas/mathematics/high-school/c6w29wxj0b2oo7vrdiio338n0ilm3e8qtb.png)
Substituting this value in equation (2), we will get:
![700-10y+5y=600](https://img.qammunity.org/2021/formulas/mathematics/high-school/q011hm4tzrjafogls08qn9smxanf6hhb1i.png)
![700-5y=600](https://img.qammunity.org/2021/formulas/mathematics/high-school/vqfo0a355587phjrks6xo6n71kbdnzx37v.png)
![700-700-5y=600-700](https://img.qammunity.org/2021/formulas/mathematics/high-school/e0kc9wxmsnuhw4a9nq1ucp9sb22gztb64f.png)
![-5y=-100](https://img.qammunity.org/2021/formulas/mathematics/high-school/sc9e78fd730qp364s8hi6jdwu5zd2dbhrg.png)
![(-5y)/(-5)=(-100)/(-5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/pzswshc1dsbertzkcb0tbbsn6w7cz85k58.png)
![y=20](https://img.qammunity.org/2021/formulas/mathematics/middle-school/udau9o6tgq4xf1w9oy0hulzequjbjnigjd.png)
Therefore, 20 wrenches were sold.
Now, we will substitute
in equation (1) as:
![x+20=70](https://img.qammunity.org/2021/formulas/mathematics/high-school/ftqgxs6ccm9zpcwvhwz35wd32mggx5ccsa.png)
![x+20-20=70-20](https://img.qammunity.org/2021/formulas/mathematics/high-school/zduokm7x6tzvtxfrwdy52179clsy6371oy.png)
![x=50](https://img.qammunity.org/2021/formulas/mathematics/middle-school/yglaf3tevccx4ke49yr22xncy14u04yts1.png)
Therefore, 50 hammers were sold.