Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. An employee at an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled 9 small baskets and 5 large baskets, using a total of 180 pieces of fruit. Using wire baskets, the employee assembled 2 small baskets and 8 large baskets, using a total of 164 pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each? The small baskets each include _____ pieces and the large ones each include _____ pieces.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  An employee at an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled 9 small baskets and  5 large baskets, using a total of 180 pieces of fruit. Using wire baskets, the employee assembled 2 small baskets and  8 large baskets, using a total of 164 pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each?  The small baskets each include _____ pieces and the large ones each include _____ pieces.

Bytelearn · Accepted Answer

Form Equations: Let's denote the number of pieces of fruit in each small basket as s and in each large basket as l. We can write two equations based on the information given:  For wicker baskets: 9s + 5l = 180 (1)  For wire baskets: 2s + 8l = 164 (2)  We will use these two equations to form a system of equations that we can solve using the elimination method.Elimination Method: To use elimination, we need to make the coefficients of one of the variables the same in both equations. Let's multiply equation (1) by 2 to match the coefficient of s in equation (2).  Multiplying equation (1) by 2, we get: 18s + 10l = 360 (3)  Now we have: 2s + 8l = 164 (2) 18s + 10l = 360 (3)Multiply and Subtract: Next, we will subtract equation (2) from equation (3) to eliminate s and solve for l.  (18s + 10l) - (2s + 8l) = 360 - 164 16s + 2l = 196  This simplifies to: 2l = 196 - 16s  Since we don't have a value for s yet, we made a mistake. We should have eliminated s completely by subtracting the entire equation (2) from equation (3).

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