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Bronze is an alloy that is made of zinc, tin, and copper in a specified proportion. Suppose an...

Question:

Bronze is an alloy that is made of zinc, tin, and copper in a specified proportion. Suppose an order is placed for 1000 pounds of bronze. The amount of tin in this order of bronze is two times the amount of zinc, and the amount of copper is 10 pounds more than 15 times the amount of tin. Find the number of pounds of zinc, tin, and copper.

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:

Total weight of alloy is {eq}1000\ lb {/eq}

Let the weight of Zinc is {eq}z\ lb {/eq}, then the weight of Tin is {eq}2z \ lb {/eq} and the weight of copper is {eq}15z +10 \ lb {/eq}

$$Weight_{zinc} + Weight_{tin} + Weight_{copper} = Weight_{total} $$

$$z + 2z + 15z + 10 =1000 $$

$$18z =1000 - 10 $$

$$18z =990 $$

$$z = 55 $$

Weight of zinc is {eq}55\ lb {/eq}, tin is {eq}(2\times 55=) 110\ lb {/eq} and that of copper is {eq}(15\times 55 +10 =) 855\ lb {/eq}


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