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A roadside vegetable stand sells pumpkins for $5 each and squash for $3 each. 1 day, they sold 6...

Question:

A roadside vegetable stand sells pumpkins for {eq}$5 {/eq} each and squash for {eq}$3 {/eq} each. {eq}1 {/eq} day, they sold {eq}6 {/eq} more squash than pumpkins and their sales totaled {eq}$98.00 {/eq}.

Write a system of equations to find the number of pumpkins and squash they sold.

Algebraic equation word problems

An algebraic equation is formed when a relation between any variable is equated to a constant.

For example: 4x +3y = 1 is an algebraic equation where x and y are variables and 1 is the equivalent constant of the relation shown in the equation.

In the word problems of algebraic equation, this relation is given in statement and we need to form an algebraic equation out of it. Assuming a base variable and determining other unknowns in its term also helps in simplifying the equation.

Answer and Explanation:

Let the number of Pumpkins and Squash are {eq}p {/eq} and {eq}s. {/eq}

According to the problem: they sold 6 more squash than pumpkins

$$s= p+ 6 $$

Total money earned {eq}$98. {/eq}

$$5p + 3s = 98 $$

Substituting value of {eq}s=p+6 {/eq}

$$5p + 3(p+6) = 98 $$

$$5p + 3p+18 = 98 $$

$$8p= 98 -18 $$

$$8p = 80 $$

$$p = 10 $$

Using the value of {eq}p {/eq} in the equation {eq}s=p + 6 {/eq}

$$s= p+ 6 $$

$$s= 10+ 6 $$

$$s= 16 $$

the number of Pumpkins and Squash are {eq}10 {/eq} and {eq}16. {/eq}


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